{"id":15,"date":"2025-10-22T01:45:51","date_gmt":"2025-10-22T01:45:51","guid":{"rendered":"https:\/\/sites.massey.ac.nz\/djws\/?page_id=15"},"modified":"2026-03-12T02:14:55","modified_gmt":"2026-03-12T02:14:55","slug":"publications","status":"publish","type":"page","link":"https:\/\/sites.massey.ac.nz\/djws\/publications\/","title":{"rendered":"Publications"},"content":{"rendered":"\n<p>\n<ul>\n        <li>\n                D.J.W. Simpson<br \/>\n                Second-order Filippov systems: sliding dynamics without sliding regions.<br \/>\n                Submitted to <i>J Diff. Eq.<\/i>\n                <a href=\"https:\/\/arxiv.org\/abs\/2603.10333\"> arXiv <\/a>\n        <\/li>\n        <li>\n                D.J.W. Simpson and I. Ghosh.<br \/>\n                Resonant grazing bifurcations revisited.<br \/>\n                Submitted to <i>SIAM J. Appl. Dyn. Syst.<\/i>\n                <a href=\"https:\/\/arxiv.org\/abs\/2602.22797\"> arXiv <\/a>\n        <\/li>\n        <li>\n                D.J.W. Simpson.<br \/>\n                The stability of boundary equilibria of three-dimensional Filippov systems.<br \/>\n                Submitted to <i>Nonlin. Anal. Hybrid Syst.<\/i>\n                <a href=\"https:\/\/arxiv.org\/abs\/2602.08536\"> arXiv <\/a>\n        <\/li>\n        <li>\n                D.J.W. Simpson and V. Avrutin.<br \/>\n                From two-dimensional continuous maps to one-dimensional discontinuous maps: a novel reduction explaining complex bifurcation structures in piecewise-linear families of maps.<br \/>\n                Submitted to <i>Nonlinearity<\/i>.\n                <a href=\"https:\/\/arxiv.org\/abs\/2512.02291\"> arXiv <\/a>\n        <\/li>\n\t<li>\n\t\tI. Ghosh and D.J.W. Simpson.<br \/>\n\t\tThe VIVID Function for Numerically Continuing Periodic Orbits arising from Grazing Bifurcations of Hybrid Dynamical Systems.<br \/>\n\t\tSubmitted to <i>J. Comput. Dyn.<\/i>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/2510.16218\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tH. Tang, A. Champneys, and D.J.W. Simpson.<br \/>\n\t\tBoundary Equilibrium Bifurcations Creating Multiple Limit Cycles in Impacting Hybrid Systems.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1137\/24M1716598\">\n\t\t<i>SIAM J. Appl. Dyn. Syst.<\/i>, 24(4):2734-2766, 2025.<\/a>\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2412.06911\"> arXiv <\/a>\t\n\t<\/li>\n\t<li>\n\t\tP.A. Glendinning and D.J.W. Simpson.<br \/>\n\t\tExtended Normal Forms for One-Dimensional Border-Collision Bifurcations.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1088\/1361-6544\/ae0b27\">\n\t\t<i>Nonlinearity<\/i>, 38(10):105012, 2025.<\/a>\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2407.16865\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tI. Ghosh and D.J.W. Simpson.<br \/>\n\t\tRobust chaos in R<sup>n<\/sup>.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1088\/1361-6544\/ae0114\">\n\t\t<i>Nonlinearity<\/i>, 38(9):095013, 2025.<\/a>\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2410.22563\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tA Piecewise-Linear Fixed Point Theorem.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1080\/00029890.2025.2495534\">\n\t\t<i>Amer. Math. Month.<\/i>, 132(7):695-699, 2025.<\/a>\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2412.11118\"> arXiv <\/a>\t\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson<br \/>\n\t\tHow to Compute Multi-Dimensional Stable and Unstable Manifolds of Piecewise-Linear Maps.\n                In: Elaydi, S. and Gardini, L. and Tikjha, W. (eds).\n\t\tNew Developments in Discrete Dynamical Systems, Difference Equations, and Applications, ICDEA 2023.<br \/>\n\t\t<a href=\"https:\/\/link.springer.com\/chapter\/10.1007\/978-3-031-82003-8_1\">\n\t\tSpringer Proceedings in Mathematics &amp; Statistics, 485:1-14, 2025.<\/a>\t\t\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2310.09941\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tThree Forms of Dimension Reduction for Border-Collision Bifurcations.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1016\/j.physleta.2025.130603\">\n\t\t<i>Phys. Lett. A<\/i>, 550:130603, 2025.<\/a>\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2412.11114\"> arXiv <\/a>\t\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tThe Two-Dimensional Border-Collision Normal Form with a Zero Determinant.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1137\/24M1683548\">\n\t\t<i>SIAM J. Appl. Dyn. Syst.<\/i>, 24(3): 2205-2245, 2025.<\/a>\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2408.04790\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tNonsmooth Folds as Tipping Points.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1063\/5.0222291\">\n\t\t<i>Chaos<\/i>, 35(2):023125, 2025.<\/a>\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2406.04587\"> arXiv <\/a>\t\n\t<\/li>\n\t<li>\n\t\tI. Ghosh, R.I. McLachlan and D.J.W. Simpson.<br \/>\n\t\tRobust Chaos in Orientation-Reversing and Non-Invertible Two-Dimensional Piecewise-Linear Maps.<br \/>\n\t\t<a href=\"https:\/\/link.springer.com\/article\/10.1007\/s00332-024-10113-8\">\n\t\t<i> J. Nonlin. Sci.<\/i>, 35:16, 2025.<\/a>\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2307.05144\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tI. Ghosh, R.I. McLachlan and D.J.W. Simpson.<br \/>\n\t\tThe Bifurcation Structure within Robust Chaos for Two-Dimensional Piecewise-Linear Maps.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1016\/j.cnsns.2024.108025\">\n\t\t<i>Commun. Nonlin. Sci. Numer. Simul.<\/i>, 134: 108025, 2024.<\/a>\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2402.05393\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tThe Necessity of the Sausage-String Structure for Mode-Locking Regions of Piecewise-Linear Maps.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1016\/j.physd.2024.134142\">\n\t\t<i>Phys. D<\/i>, 462: 134142, 2024.<\/a>\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2312.03887\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson and P.A. Glendinning.<br \/>\n\t\tInclusion of Higher-Order Terms in the Border-Collision Normal Form: Persistence of Chaos and Applications to Power Converters.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1016\/j.physd.2024.134131\">\n\t\t<i> Phys. D<\/i>, 462: 134131, 2024.<\/a>\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2111.12222\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tP.A. Glendinning and D.J.W. Simpson.<br \/>\n\t\tDifferentiable Conjugacies for One-Dimensional Maps.\n\t\tIn: Olaru, S., Cushing, J., Elaydi, S., Lozi, R. (eds).\n\t\tDifference Equations, Discrete Dynamical Systems and Applications, ICDEA 2022.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1007\/978-3-031-51049-6_6\">\n\t\tSpringer Proceedings in Mathematics &amp; Statistics, 444:115-130, 2024.<\/a>\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2303.00115\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tBorder-Collision Bifurcations from Stable Fixed Points to Any Number of Coexisting Chaotic Attractors.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1080\/10236198.2023.2265495\">\n\t\t<i>J. Difference Eq. Appl.<\/i>, 30(1): 90-110, 2024.<\/a>\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2207.10251\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tDetecting Invariant Expanding Cones for Generating Word Sets to Identify Chaos in Piecewise-Linear Maps.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1080\/10236198.2022.2070009\">\n\t\t<i>J. Difference Eq. Appl.<\/i>, 29:1094-1126, 2023.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/2010.08241\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tP.A. Glendinning and D.J.W. Simpson.<br \/>\n\t\tUnstable Dimension Variability and Heterodimensional Cycles in the Border-Collision Normal Form.<br \/>\n\t\t<a href=\"https:\/\/journals.aps.org\/pre\/abstract\/10.1103\/PhysRevE.108.L022202\">\n\t\t<i>Phys. Rev. E.<\/i>, 108(2):L022202, 2023.<\/a>\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2211.05917\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tH.O. Fatoyinbo and D.J.W. Simpson.<br \/>\n\t\tA Synopsis of the Non-Invertible, Two-Dimensional, Border-Collision Normal Form with Applications to Power Converters.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1142\/S0218127423300197\">\n\t\t<i>Int. J. Bifurcation Chaos<\/i>, 33(8):2330019, 2023.<\/a>\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2210.14445\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tP.A. Glendinning and D.J.W. Simpson.<br \/>\n\t\tNormal Forms, Differentiable Conjugacies and Elementary Bifurcations of Maps.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1137\/22M1503701\">\n\t\t<i>SIAM J. Appl. Math.<\/i>, 83(2):816-836, 2023.<\/a>\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2206.04840\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tI. Belykh, R. Kuske, M. Porfini and D.J.W. Simpson.<br \/>\n\t\tBeyond the Bristol Book: Advances and Perspectives in Non-Smooth Dynamics and Applications. (an editorial)<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1063\/5.0138169\"><i>Chaos<\/i>, 33(1):010402, 2023.<\/a>\n\t\t<a href=\"https:\/\/math.gsu.edu\/ibelykh\/2022_Chaos_Beyond.pdf\"> preprint <\/a><br \/>\n\t<\/li>\n\t<li>\n\t\tP.A. Glendinning and D.J.W. Simpson.<br \/>\n\t\tNormal Forms for Saddle-Node Bifurcations: Takens&#8217; Coefficient and Applications in Climate Models.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1098\/rspa.2022.0548\">\n\t\t<i>Proc. R. Soc. A<\/i>, 478:20220548, 2022.<\/a>\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2208.09633\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tP.A. Glendinning and D.J.W. Simpson.<br \/>\n\t\tChaos in the Border-Collision Normal Form: A Computer-Assisted Proof Using Induced Maps and Invariant Expanding Cones.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1016\/j.amc.2022.127357\">\n\t\t<i>Appl. Math. Comput.<\/i>, 434:127357, 2022.<\/a>\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2108.05999\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tI. Ghosh and D.J.W. Simpson.<br \/>\n\t\tRenormalisation of the Two-Dimensional Border-Collision Normal Form.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1142\/S0218127422501814\">\n\t\t<i>Int. J. Bifurcation Chaos<\/i>, 32(12):2250181, 2022.<\/a>\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2109.09242\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tH.O. Fatoyinbo, R.G. Brown, D.J.W. Simpson and B. van Brunt.<br \/>\n\t\tPattern Formation in a Spatially-Extended Model of Pacemaker Dynamics in Smooth Muscle Cells.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1007\/s11538-022-01043-1\">\n\t\t<i>Bull. Math. Biol.<\/i>, 84(8):86, 2022.<\/a>\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2111.00168\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tDimension Reduction for Slow-Fast, Piecewise-Linear ODEs and Obstacles to a General Theory.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1016\/j.physd.2022.133368\">\n\t\t<i>Phys. D<\/i>, 439:133368, 2022.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1801.04653\"> arXiv <\/a>\n\t<\/li>\n\t<li>\t\n\t\tS.S. Muni, R.I. McLachlan and D.J.W. Simpson.<br \/>\n\t\tUnfolding Globally Resonant Homoclinic Tangencies.<br \/>\n\t\t<a href=\"https:\/\/www.aimsciences.org\/article\/doi\/10.3934\/dcds.2022043\">\n\t\t<i>Discrete Contin. Dyn. Syst.<\/i>, 42(8):4013-4030, 2022.<\/a>\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2108.07476\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tTwenty Hopf-Like Bifurcations in Piecewise-Smooth Dynamical Systems.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1016\/j.physrep.2022.04.007\">\n\t\t<i>Phys. Rep.<\/i>, 970:1-80, 2022.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1905.01329\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tI. Ghosh and D.J.W. Simpson.<br \/>\n\t\tRobust Devaney Chaos in the Two-Dimensional Border-Collision Normal Form.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1063\/5.0079807\">\n\t\t<i>Chaos<\/i>, 32:043120, 2022.<\/a>\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2111.12893\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tOn the Stability of Boundary Equilibria in Filippov Systems.<br \/>\n\t\t<a href=\"https:\/\/www.aimsciences.org\/article\/doi\/10.3934\/cpaa.2021097\">\n\t\t<i>Commun. Pure Appl. Anal.<\/i>, 20(9):3093-3111, 2021.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/2101.04214\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tS.S. Muni, R.I. McLachlan and D.J.W. Simpson.<br \/>\n\t\tHomoclinic Tangencies with Infinitely Many Asymptotically Stable Single-Round Periodic Solutions.<br \/>\n\t\t<a href=\"https:\/\/www.aimsciences.org\/article\/doi\/10.3934\/dcds.2021010\">\n\t\t<i>Discrete Contin. Dyn. Syst.<\/i>, 41(8):3629-3650, 2021.<\/a>\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2006.01405\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tP.A. Glendinning and D.J.W. Simpson.<br \/>\n\t\tA Constructive Approach to Robust Chaos using Invariant Manifolds and Expanding Cones.<br \/>\n\t\t<a href=\"https:\/\/www.aimsciences.org\/article\/doi\/10.3934\/dcds.2020409\">\n\t\t<i>Discrete Contin. Dyn. Syst.<\/i>, 41(7):3367-3387, 2021.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1906.11969\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tP.A. Glendinning and D.J.W. Simpson.<br \/>\n\t\tRobust Chaos and the Continuity of Attractors.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1093\/imatrm\/tnaa002\">\n\t\t<i>Trans. Math. Appl.<\/i>, 4(1):tnaa002, 2020.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1906.11974\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tChaotic Attractors from Border-Collision Bifurcations:\n\t\tStable Border Fixed Points and Determinant-Based Lyapunov Exponent Bounds.<br \/>\n\t\t<a href=\"https:\/\/www.nzjmath.org\/index.php\/NZJMATH\/article\/view\/65\">\n\t\t<i>NZJM<\/i>, 50:71-91, 2020.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1911.04578\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson, V. Avrutin and S. Banerjee.<br \/>\n\t\tThe Nordmark Map and the Problem of Large-Amplitude Chaos in Impact Oscillators.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1103\/PhysRevE.102.022211\">\n\t\t<i>Phys. Rev. E<\/i>, 102:022211, 2020.<\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tThe Stability of Fixed Points on Switching Manifolds of Piecewise-Smooth Continuous Maps.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1007\/s10884-019-09803-9\">\n\t\t<i>J. Dyn. Diff. Equat.<\/i>, 32(3):1527-1552, 2020.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1612.02932\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tH.O. Fatoyinbo, R.G. Brown, D.J.W. Simpson and B. van Brunt.<br \/>\n\t\tNumerical Bifurcation Analysis of Pacemaker Dynamics in a Model of Smooth Muscle Cells.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1007\/s11538-020-00771-6\">\n\t\t<i>Bull. Math. Biol.<\/i>, 82(7):95, 2020.<\/a>\n\t\t<a href=\"https:\/\/arxiv.org\/abs\/2004.00343\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tUnfolding Codimension-Two Subsumed Homoclinic Connections in Two-Dimensional Piecewise-Linear Maps.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1142\/S0218127420300062\">\n\t\t<i>Int. J. Bifurcation Chaos<\/i>, 30(3):2030006, 2020.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1907.02653\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tHopf-Like Boundary Equilibrium Bifurcations involving Two Foci in Filippov Systems.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1016\/j.jde.2019.06.016\">\n\t\t<i>J. Diff. Eq.<\/i>, 267(11):6133-6151, 2019.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1812.03587\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tM.E. Roberts, C. Kueh, E. Greenbank, D. Clarke, S. van Hove, D.J.W. Simpson, A. Williams and J. Williams.<br \/>\n\t\tModelling the Mechanical Action of a Front Loading Washing Machine.\n                Proceedings of the 2017 Mathematics and Statistics in Industry NZ Study Group, MINZ-2017.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.21914\/anziamj.v59i0.13473\">\n\t\t<i> ANZIAM J.<\/i>, 59: M30-M62, 2019.<\/a><br \/>\n\t<\/li>\n\t<li>\n\t\tH.A. Al Fran, D.J.W. Simpson and C.P. Tuffley.<br \/>\n\t\tCharacterisation and Classification of Signatures of Spanning Trees of the n-Cube.<br \/>\n\t\t<a href=\"http:\/\/ajc.maths.uq.edu.au\/pdf\/75\/ajc_v75_p259.pdf\">\n\t\t<i>Australas. J. Combin.<\/i>, 75(3):259-295, 2019.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1807.11183\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tA General Framework for Boundary Equilibrium Bifurcations of Filippov Systems.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1063\/1.5037947\">\n\t\t<i>Chaos<\/i>, 28(10):103114, 2018.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1804.11036\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tA Compendium of Hopf-Like Bifurcations in Piecewise-Smooth Dynamical Systems.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1016\/j.physleta.2018.06.004\">\n\t\t<i>Phys. Lett. A<\/i>, 382(35):2439-2444, 2018.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1804.11009\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tM.R. Jeffrey, G. Kafanas and D.J.W. Simpson.<br \/>\n\t\tJitter in Dynamical Systems with Intersecting Discontinuity Surfaces.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1142\/S0218127418300203\">\n\t\t<i>Int. J. Bifurcation Chaos<\/i>, 28(6):1830020, 2018.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1610.03976\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tThe Structure of Mode-Locking Regions of Piecewise-Linear Continuous Maps: II. Skew Sawtooth Maps.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1088\/1361-6544\/aaa7bb\">\n\t\t<i>Nonlinearity<\/i>, 31(5):1905-1939, 2018.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1612.03968\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson and R. Kuske.<br \/>\n\t\tThe Influence of Localised Randomness on Regular Grazing Bifurcations with Applications to Impacting Dynamics.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1177\/1077546316642054\">\n\t\t<i>J. Vib. Contr.<\/i>, 24(2):407-426, 2018.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1502.02724\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tGrazing-Sliding Bifurcations Creating Infinitely Many Attractors.<br \/>\n\t\t<a href=\"https:\/\/doi.org\/10.1142\/S0218127417300427\">\n\t\t<i>Int. J. Bifurcation Chaos<\/i>, 27(12):1730042, 2017.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1705.10931\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tOpen Problems on Border-Collision Bifurcations.\n\t\tIn: Colombo A., Jeffrey M., L\u00e1zaro J., Olm J. (eds).\n                Proceedings from the workshop: Advances in Nonsmooth Dynamics, CRM, Barcelona, Feb-Apr, 2016.<br \/>\n\t\t<a href=\"https:\/\/link.springer.com\/chapter\/10.1007\/978-3-319-55642-0_29\">\n\t\tExtended Abstracts Spring 2016. 8:163-166, 2017.<\/a><br \/>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson and C.P. Tuffley.<br \/>\n\t\tSubsumed Homoclinic Connections and Infinitely Many Coexisting Attractors in Piecewise-Linear Maps.<br \/>\n\t\t<a href=\"http:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127417300105\">\n\t\t<i>Int. J. Bifurcation Chaos<\/i>, 27(2):1730010, 2017.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1611.00067\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tThe Structure of Mode-Locking Regions of Piecewise-Linear Continuous Maps: I. Nearby Mode-Locking Regions and Shrinking Points.<br \/>\n\t\t<a href=\"http:\/\/iopscience.iop.org\/article\/10.1088\/1361-6544\/aa4f49\/meta;jsessionid=8AD1C2471D41CDE104616EA2BB4D7096.c2.iopscience.cld.iop.org\">\n\t\t<i>Nonlinearity<\/i>, 30(1):382-444, 2017.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1510.01416\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tThe Instantaneous Local Transition of a Stable Equilibrium to a Chaotic Attractor in Piecewise-Smooth Systems of Differential Equations.<br \/>\n\t\t<a href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0375960116304443\">\n\t\t<i>Phys. Lett. A<\/i>, 380(38):3067-3072, 2016.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1606.00073\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tUnfolding Homoclinic Connections formed by Corner Intersections in Piecewise-Smooth Maps.<br \/>\n\t\t<a href=\"http:\/\/scitation.aip.org\/content\/aip\/journal\/chaos\/26\/7\/10.1063\/1.4954876\">\n\t\t<i>Chaos<\/i>, 26:073105, 2016.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1603.04932\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tBorder-Collision Bifurcations in R<sup>N<\/sup>.<br \/>\n\t\t<a href=\"http:\/\/epubs.siam.org\/doi\/10.1137\/15M1006982\">\n\t\t<i>SIAM Rev.<\/i>, 58(2):177-226, 2016.<\/a>\n\t\t<a href=\"BCBreview_earlyVersion.pdf\"> preprint <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson and M.R. Jeffrey.<br \/>\n\t\tFast Phase Randomisation via Two-Folds.<br \/>\n\t\t<a href=\"http:\/\/rspa.royalsocietypublishing.org\/content\/472\/2186\/20150782.abstract\">\n\t\t<i>Proc. R. Soc. A<\/i>, 472(2186):20150782, 2016.<\/a>\n\t\t(open access)\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson and R. Kuske.<br \/>\n\t\tStochastic Perturbations of Periodic Orbits with Sliding.<br \/>\n\t\t<a href=\"http:\/\/link.springer.com\/article\/10.1007\/s00332-015-9248-7\">\n\t\t<i>J. Nonlin. Sci.<\/i>, 25(4):967-1014, 2015.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1404.6845\"> arXiv <\/a>\n\t<\/li>\n        <li>\n\t        D.J.W. Simpson and R. Kuske.<br \/>\n\t\tThe Positive Occupation Time of Brownian Motion with Two-Valued Drift and Asymptotic Dynamics of Sliding Motion with Noise.<br \/>\n\t\t<a href=\"http:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0219493714500105\">\n\t\t<i>Stoch. Dyn.<\/i>, 14(4):1450010, 2014.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1204.5985\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t        D.J.W. Simpson and R. Kuske.<br \/>\n\t\tStochastically Perturbed Sliding Motion in Piecewise-Smooth Systems.<br \/>\n\t\t<a href=\"http:\/\/www.aimsciences.org\/journals\/displayArticlesnew.jsp?paperID=10300\">\n\t\t<i>Discrete Contin. Dyn. Syst. Ser. B<\/i>, 19(9):2889-2913, 2014.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1204.5792\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tOn the Relative Coexistence of Fixed Points and Period-Two Solutions near Border-Collision Bifurcations.<br \/>\n\t\t<a href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0893965914002468\">\n\t\t<i>Appl. Math. Lett.<\/i>, 38:162-167, 2014.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1405.7083\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tScaling Laws for Large Numbers of Coexisting Attracting Periodic Solutions in the Border-Collision Normal Form.<br \/>\n\t\t<a href=\"http:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127414501181\">\n\t\t<i>Int. J. Bifurcation Chaos<\/i>, 24(9):1450118, 2014.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1403.4678\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tSequences of Periodic Solutions and Infinitely Many Coexisting Attractors in the Border-Collision Normal Form.<br \/>\n\t\t<a href=\"http:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S0218127414300183?af=R\">\n\t\t<i>Int. J. Bifurcation Chaos<\/i>, 24(6):1430018, 2014.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1312.2651\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tM.R. Jeffrey and D.J.W. Simpson.<br \/>\n\t\tNon-Filippov Dynamics Arising from the Smoothing of Nonsmooth Systems, and its Robustness to Noise.<br \/>\n\t\t<a href=\"http:\/\/link.springer.com\/article\/10.1007\/s11071-013-1217-9\">\n\t\t<i>Nonlinear Dyn.<\/i>, 76(2):1395-1410, 2014.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1310.8328\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson.<br \/>\n\t\tOn Resolving Singularities of Piecewise-Smooth Discontinuous Vector Fields via Small Perturbations.<br \/>\n\t\t<a href=\"https:\/\/www.aimsciences.org\/journals\/displayArticlesnew.jsp?paperID=9776\">\n\t\t<i>Discrete Contin. Dyn. Syst.<\/i>, 34(9):3803-3830, 2014.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1304.4317\"> arXiv <\/a>\n\t<\/li>\n        <li>\n\t        D.J.W. Simpson, S.J. Hogan and R. Kuske.<br \/>\n\t\tStochastic Regular Grazing Bifurcations.<br \/>\n\t\t<a href=\"http:\/\/epubs.siam.org\/doi\/abs\/10.1137\/120884286\">\n\t\t<i> SIAM J. Appl. Dyn. Syst.<\/i>, 12(2), 533-559, 2013.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1207.2703\"> arXiv <\/a>\n\t<\/li>\n        <li>\n                D.J.W. Simpson and J.D. Meiss.<br \/>\n                Aspects of Bifurcation Theory for Piecewise-Smooth, Continuous Systems.<br \/>\n\t\t<a href=\"http:\/\/dx.doi.org\/10.1016\/j.physd.2011.05.002\">\n\t\t<i> Phys. D<\/i>, 241(22):1861-1868, 2012.<\/a>\n                <a href=\"http:\/\/arxiv.org\/abs\/1006.4123\"> arXiv <\/a>\n        <\/li>\n\t<li>\n\t        D.J.W. Simpson, R. Kuske and Y.-X. Li.<br \/>\n\t\tDynamics of Simple Balancing Models with Time-Delayed Switching Feedback Control.<br \/>\n\t\t<a href=\"http:\/\/www.springerlink.com\/content\/414775187x170552\">\n\t\t<i> J. Nonlin. Sci.<\/i>, 22(2):135-167, 2012.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1104.1446\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson and R. Kuske.<br \/>\n\t\tMixed-Mode Oscillations in a Stochastic Piecewise-Linear System.<br \/>\n\t\t<a href=\"http:\/\/www.sciencedirect.com\/science\/article\/pii\/S0167278911001047\">\n\t\t<i> Phys. D<\/i>, 240:1189-1198, 2011.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1010.1504\"> arXiv <\/a>\n\t<\/li>\n        <li>\n\t\tD.J.W. Simpson.<br \/>\n                <a href=\"https:\/\/www.worldscientific.com\/worldscibooks\/10.1142\/7612\">Bifurcations in Piecewise-Smooth Continuous Systems.<\/a><br \/>\n\t\tWorld Scientific, Singapore, 2010.<br \/>\n                <img decoding=\"async\" src=\"http:\/\/sites.massey.ac.nz\/djws\/wp-content\/uploads\/sites\/177\/2025\/10\/Si10cover.jpg\" width=\"80\">\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson and J.D. Meiss.<br \/>\n\t\tResonance near Border-Collision Bifurcations in Piecewise-Smooth, Continuous Maps.<br \/>\n\t\t<a href=\"http:\/\/iopscience.iop.org\/0951-7715\/23\/12\/006\">\n\t\t<i> Nonlinearity<\/i>, 23(12):3091-3118, 2010.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/1002.2237\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson and J.D. Meiss.<br \/>\n\t\tSimultaneous Border-Collision and Period-Doubling Bifurcations.<\/br>\n\t\t<a href=\"http:\/\/scitation.aip.org\/getpdf\/servlet\/GetPDFServlet?filetype=pdf&amp;id=CHAOEH000019000003033146000001&amp;idtype=cvips&amp;prog=normal\">\n\t\t<i> Chaos<\/i>, 19(3):033146, 2009.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/0905.3730\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson and J.D. Meiss.<br \/>\n\t\tShrinking Point Bifurcations of Resonance Tongues for Piecewise-Smooth, Continuous Maps.<br \/>\n\t        <a href=\"http:\/\/iopscience.iop.org\/0951-7715\/22\/5\/009\">\n\t\t<i> Nonlinearity<\/i>, 22(5):1123-1144, 2009.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/0809.3510\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson, D.S. Kompala and J.D. Meiss.<br \/>\n\t\tDiscontinuity Induced Bifurcations in a Model of <i> Saccharomyces cerevisiae<\/i>.<br \/>\n\t\t<a href=\"http:\/\/www.sciencedirect.com\/science?_ob=ArticleURL&amp;_udi=B6VHX-4V7MSWJ-1&amp;_user=918210&amp;_coverDate=03%2F31%2F2009&amp;_rdoc=6&amp;_fmt=high&amp;_orig=browse&amp;_srch=doc-info(%23toc%236078%232009%23997819998%23932124%23FLA%23display%23Volume)&amp;_cdi=6078&amp;_sort=d&amp;_docanchor=&amp;_ct=9&amp;_acct=C000047944&amp;_version=1&amp;_urlVersion=0&amp;_userid=918210&amp;md5=41521ee65ce59f5a9e3aa873d2eb85b4\">\n\t\t<i> Math. Biosci.<\/i>, 218(1):40-49, 2009.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/0807.0249\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson and J.D. Meiss.<br \/>\n\t\tUnfolding a Codimension-Two Discontinuous Andronov-Hopf Bifurcation.<br \/>\n\t        <a href=\"http:\/\/chaos.aip.org\/resource\/1\/chaoeh\/v18\/i3\/p033125_s1\">\n\t\t<i> Chaos<\/i>, 18(3):033125, 2008.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/0804.3101\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson and J.D. Meiss.<br \/>\n\t\tNeimark-Sacker Bifurcations in Planar, Piecewise-Smooth, Continuous Maps.<br \/>\n\t\t<a href=\"http:\/\/scitation.aip.org\/getabs\/servlet\/GetabsServlet?prog=normal&amp;id=SJADAY000007000003000795000001&amp;idtype=cvips&amp;gifs=yes\">\n\t\t<i> SIAM J. Appl. Dyn. Syst.<\/i>, 7(3):795-824, 2008.<\/a>\n\t<\/li>\n        <li>\n                B. Marts, D.J.W. Simpson, A. Hagberg and A.L. Lin.<br \/>\n                Period Doubling in a Periodically Forced Belousov-Zhabotinsky Reaction.<br \/>\n                <a href=\"http:\/\/scitation.aip.org\/getabs\/servlet\/GetabsServlet?prog=normal&amp;id=PLEEE8000076000002026213000001&amp;idtype=cvips&amp;gifs=yes\">\n                <i> Phys. Rev. E<\/i>, 76(2):026213, 2007. <\/a>\n        <\/li>\n\t<li>\n\t\tD.J.W. Simpson and J.D. Meiss.<br \/>\n\t\tAndronov-Hopf Bifurcations in Planar, Piecewise-Smooth, Continuous Flows.<br \/>\n\t\t<a href=\"http:\/\/www.sciencedirect.com\/science?_ob=ArticleURL&amp;_udi=B6TVM-4P1P6S8-1&amp;_user=918210&amp;_rdoc=1&amp;_fmt=&amp;_orig=search&amp;_sort=d&amp;view=c&amp;_acct=C000047944&amp;_version=1&amp;_urlVersion=0&amp;_userid=918210&amp;md5=1a7eb55a888744c604ea09347c85f774\">\n\t\t<i> Phys. Lett. A<\/i>, 371(3):213-220, 2007.<\/a>\n\t\t<a href=\"http:\/\/arxiv.org\/abs\/nlin\/0701036\"> arXiv <\/a>\n\t<\/li>\n\t<li>\n\t\tD.J.W. Simpson, V. Kirk and J. Sneyd.<br \/>\n\t\tComplex Oscillations and Waves of Calcium in Pancreatic Acinar Cells.<br \/>\n\t\t<a href=\"http:\/\/www.sciencedirect.com\/science?_ob=ArticleURL&amp;_udi=B6TVK-4F31PY2-3&amp;_user=918210&amp;_rdoc=1&amp;_fmt=&amp;_orig=search&amp;_sort=d&amp;view=c&amp;_acct=C000047944&amp;_version=1&amp;_urlVersion=0&amp;_userid=918210&amp;md5=ebd4bbf7426afa02beb3cbd4a3829fdc\">\n\t\t<i> Phys. D<\/i>, 200:303-324, 2005. <\/a>\n\t<\/li>\n<\/ul>\n<\/p>\n","protected":false},"excerpt":{"rendered":"<p>D.J.W. Simpson Second-order Filippov systems: sliding dynamics without sliding regions. Submitted to J Diff. Eq. arXiv D.J.W. Simpson and I. Ghosh. Resonant grazing bifurcations revisited. Submitted to SIAM J. Appl. Dyn. Syst. arXiv D.J.W. Simpson. The stability of boundary equilibria &hellip; <a href=\"https:\/\/sites.massey.ac.nz\/djws\/publications\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":314,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-15","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.massey.ac.nz\/djws\/wp-json\/wp\/v2\/pages\/15","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.massey.ac.nz\/djws\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.massey.ac.nz\/djws\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.massey.ac.nz\/djws\/wp-json\/wp\/v2\/users\/314"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.massey.ac.nz\/djws\/wp-json\/wp\/v2\/comments?post=15"}],"version-history":[{"count":12,"href":"https:\/\/sites.massey.ac.nz\/djws\/wp-json\/wp\/v2\/pages\/15\/revisions"}],"predecessor-version":[{"id":155,"href":"https:\/\/sites.massey.ac.nz\/djws\/wp-json\/wp\/v2\/pages\/15\/revisions\/155"}],"wp:attachment":[{"href":"https:\/\/sites.massey.ac.nz\/djws\/wp-json\/wp\/v2\/media?parent=15"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}