Physikalische Mathematik

Multiple Coexisting Attractors in a Generalized Chua's Circuit with a Smoothly Adjustable Symmetry and Nonlinearity

Abstract

Tsafack N and Kengne J

A generalized Chua’s circuit with a single parametric nonlinearity is introduced in this letter. The circuit is obtained by replacing the Chua’s diode of the classical Chua’s circuit with a parametric active diode pair. The obtained circuit can be described by three differential equations. Preliminary dynamic properties of the circuit are categorized with respect to its parameters and it is found that the circuit has two nonzero stable node-foci leading to complex coexisting behaviours. A plethora of coexisting symmetric and asymmetric attractors are depicted. More importantly, the symmetry of the circuit can be monitored with a single parameter k (i.e. a single control resistor). Also, multistability in the symmetry boundary is discussed by monitoring the single bifurcation parameter k. Finally, Pspice circuit implementation results are consistent with the complex dynamic behaviours observed during numerical analysis.