2020/05/08 by A. Ishaq Ahamed, M. Lakshmanan, Ahamed, A. Ishaq +1
Engineering · Neuroscience · Physics and Astronomy · #Adaptation and Self-Organizing Systems (nlin.AO) #Advanced Memory and Neural Computing #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Neural dynamics and brain function #nlin.AO #nlin.CD #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.2005.04225
23 pages, 14 figures, Accepted for publication in the Int. J. Bifurcation and Chaos
arxiv created 2020/05/08 · openalex publication_date 2020/05/08 · arxiv updated 2020/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we report the occurrence of sliding bifurcations admitted by the memristive Murali-Lakshmanan-Chua circuit \citeicha13 and the memristive driven Chua oscillator \citepicha11. Both of these circuits have a flux-controlled active memristor designed by the authors in 2011, as their non-linear element. The three segment piecewise-linear characteristic of this memristor bestows on the circuits two discontinuity boundaries, dividing their phase spaces into three sub-regions. For proper choice of parameters, these circuits take on a degree of smoothness equal to one at each of their two discontinuities, thereby causing them to behave as Filippov systems. Sliding bifurcations, which are characteristic of Filippov systems, arise when the periodic orbits in each of the sub-regions, interact with the discontinuity boundaries, giving rise to many interesting dynamical phenomena. The numerical simulations are carried out after incorporating proper zero time discontinuity mapping (ZDM) corrections. These are found to agree well with the experimental observations which we report here appropriately.