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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Relaxation Oscillations and Chaos in a Duffing Type Equation: A Case Study

Discontinuity, Nonlinearity, and Complexity 5(4) (2016) 457--474 | DOI:10.5890/DNC.2016.12.010

L. Lerman; A. Kazakov; N.Kulagin

L. Lerman1, A. Kazakov2,1, N.Kulagin3

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Results of numerical simulations of a Duffing type Hamiltonian system with a slow periodically varying parameter are presented. Using theory of adiabatic invariants, reversibility of the system and theory of symplectic maps, along with thorough numerical experiments, we present many details of the orbit behavior for the system. In particular, we found many symmetric mixed mode periodic orbits, both being hyperbolic and elliptic, the regions with a perpetual adiabatic invariant and chaotic regions. For the latter region we present details of chaotic behavior: calculation of homoclinic tangles and Lyapunov exponents.


1 Institute of Information Technology, Mathematics & Mechanics, Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod, 603950, Russia 2 National Research University Higher School of Economics, Nizhny Novgorod, 603155, Russia 3 Moscow Aviation Institute (MAI), Moscow, Russia


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