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Nonlinear Sciences > Chaotic Dynamics

arXiv:1704.01167 (nlin)
[Submitted on 4 Apr 2017]

Title:Discontinuity Induced Hopf and Neimark-Sacker Bifurcations in a Memristive Murali-Lakshmanan-Chua Circuit

Authors:A. Ishaq Ahamed, M. Lakshmanan
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Abstract:We report using Clarke's concept of generalised differential and a modification of Floquet theory to non-smooth oscillations, the occurrence of discontinuity induced Hopf bifurcations and Neimark-Sacker bifurcations leading to quasiperiodic attractors in a memristive Murali-Lakshmanan-Chua (memristive MLC) circuit. The above bifurcations arise because of the fact that a memristive MLC circuit is basically a nonsmooth system by virtue of having a memristive element as its nonlinearity. The switching and modulating properties of the memristor which we have considered endow the circuit with two discontinuity boundaries and multiple equilibrium points as well. As the Jacobian matrices about these equilibrium points are non-invertible, they are non-hyperbolic, some of these admit local bifurcations as well. Consequently when these equilibrium points are perturbed, they lose their stability giving rise to quasiperiodic orbits. The numerical simulations carried out by incorporating proper discontinuity mappings (DMs), such as the Poincaré discontinuity map (PDM) and zero time discontinuity map (ZDM), are found to agree well with experimental observations.
Comments: 28 pages,18 figures
Subjects: Chaotic Dynamics (nlin.CD)
ACM classes: J.2
Cite as: arXiv:1704.01167 [nlin.CD]
  (or arXiv:1704.01167v1 [nlin.CD] for this version)
  https://doi.org/10.48550/arXiv.1704.01167
Journal reference: International Journal of Bifurcation and Chaos, Vol. 27,Number 06, June 2017

Submission history

From: Ishaq Ahamed [view email]
[v1] Tue, 4 Apr 2017 20:06:08 UTC (3,628 KB)
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