Multiple scroll attractors and multistability in the collective dynamics of a four chain coupled hopfield inertial neuron network: analysis and circuit design investigations

Abstract

This work deals with the chain bidirectional coupling of four inertial Hopfield neurons. Each of our cells taken alone is modeled by a second order differential equation having three resting points. Coupling these neurons helps increasing the number of fixed points that is related to the amount of memory assigned to the network. The system having a hyperbolic tangent as nonlinearity is investigated with the help of suitable nonlinear dynamical tools like bifurcation diagrams, Lyapunov exponent diagrams and phase portraits to resort the richness of the model. As the coupling adds the amount of equilibriums, it also helps in generating multiple scroll attractors. The system that was unable of oscillation presents firing patterns such as parallel branches, coexistence of up to sixteen attractors in the phase plane, extreme events and Hopf bifurcation to name a few. All these features are discovered when observing the coupling strengths, the dissipation coefficient and when programming initial states around sensitive equilibriums. The electronic version of the four-chain coupled inertial neurons system is provided and simulated on Pspice with the aim to confirm the results obtained in the numerical scheme.