The Effect of Symmetry Breaking in an Inertial Neural System with a Non-Monotonic Activation Function : Theoretical Study, Asymmetric Coexistence and Experimental Investigation

Multistability and symmetry breaking have been significantly investigated recently. In this paper, we study the effects of symmetry breaking on the behaviour of a particular class of inertial neural system with a non-monotonic activation function. By introducing a constant term in the nonlinearity of the model, we show that this system presents an asymmetric type dynamics marked by the coexistence of chaotic bursting oscillation according to the different membranes of the neurons. We also report some interesting phenomena such as rising voltage peaks, the coexistence of several asymmetric attractors (six, five and four), the coexistence of asymmetric bubble bifurcation and transient chaos as well. We illustrate the sensibility of symmetry breaking parameter on 2D Lyapunov exponent, plotted for three different values of symmetry control parameter. We prove that this model owns offset boosting property and amplitude total control feature. The experimental study is executed based on a microcontroller implementation and the results are in agreement with the numerical analysis