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Discontinuity-induced mixed mode oscillations for the nonsmooth Murali–Lakshmanan–Chua circuit

Yue Yu, Weinan Zhu, Wenyao Zhou and Zhenyu Chen

Vol. 18 (2023), No. 2, 277–291

We present a detailed investigation into the occurrence of complex patterns in the memristive Murali–Lakshmanan–Chua (MLC) circuit system. The nonsmooth system is divided into fast and slow subsystems by assuming a cosinusoidal function as a slow variable. The determination of the region of bifurcation space in the fast subsystem (the FS) is associated with nonsmooth boundaries and switching manifolds. The transition through the switching boundaries may give rise to complicated dynamics including coexistence of bilateral equilibrium states and jumping behaviors constituting the relaxation-type oscillation cycles. Combined with the generalized Jacobian matrix and Clarke derivative, discontinuous bifurcations of the fast subsystem at the nonsmooth boundaries are investigated. Two types of oscillation modes are obtained, and their generating mechanism is discussed. It is revealed that not only the equilibrium dynamics of the fast subsystem but also discontinuous bifurcations at switching boundaries have a deep impact on the whole system dynamic, leading to the sudden transition on two switching boundaries. Finally, performance of this nonlinear nonsmooth MLC circuit system is well verified by numerical simulations and analytical studies.

nonsmooth nonlinearity, MLC circuit, switching boundaries, mixed mode oscillations (MMOs), coupling coefficient
Received: 8 December 2022
Revised: 30 December 2022
Accepted: 7 January 2023
Published: 18 April 2023
Yue Yu
School of Science
Nantong University
Weinan Zhu
School of Science
Nantong University
Wenyao Zhou
School of Science
Nantong University
Zhenyu Chen
Department of Architecture and Civil Engineering
City University of Hong Kong
Hong Kong