May 12, 2020 1:14 ws-ijbc International Journal of Bifurcation and Chaos c  World Scientific Publishing Company SLIDING BIFURCATIONS IN THE MEMRISTIVE MURALI-LAKSHMANAN-CHUA CIRCUIT AND THE MEMRISTIVE DRIVEN CHUA OSCILLATOR A. ISHAQ AHAMED Department of Physics, Jamal Mohamed College, Tiruchirappalli-620020,India ishaq1970@gmail.com M. LAKSHMANAN Department of Nonlinear Dynamics,School of Physics, Bharathidasan University, Tiruchirappalli-620024, India lakshman@.gmail.com Received (to be inserted by publisher) In this paper we report the occurrence of sliding bifurcations admitted by the memristive Murali- Lakshmanan-Chua circuit [Ishaq & Lakshmanan, 2013] and the memristive driven Chua oscilla- tor [Ishaq et al., 2011]. 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 characteris- tic 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. Keywords : memristive MLC circuit, memristive driven Chua oscillator, Filippov system, Zero Time Discontinuity Mapping (ZDM) corrections 1. Introduction Among the nonlinear systems, there are large classes of systems called non-smooth systems or piecewise- smooth systems. These system are found to contain terms that are non-smooth functions of their arguments and fall outside the purview of the conventional theory of dynamical systems. Examples of such systems are electrical circuits which have switches, mechanical devices wherein components impact against each other and many control systems where continuous changes may trigger discrete actions. These systems have their phase-space divided into two or more sub-regions by the presence of what are called discontinuity boundaries. They are characterized by functions that are event driven, that is they are normally smooth but lose their smoothness at the discontinuity due to instantaneous events such as the application of a 1 arXiv:2005.04225v1 [nlin.AO] 8 May 2020