Symmetry and asymmetry induced dynamics in a memristive twin-T circuit

The dynamics of memristor-based chaotic oscillators with perfect symmetry is very well documented. However, the literature is relatively poor concerning the behaviour of such types of circuits when their symmetry is perturbed. In this paper, we consider the dynamics of a memristive twin-T oscillator. Here, the symmetry is broken by assuming a memristor with an asymmetric pinched hysteresis loop i - v characteristics. A variable disturbance term is introduced into the current-voltage relationship of the memristor in order to obtain an asymmetric characteristic. Phase portraits, bifurcations, basins of attraction, and Lyapunov exponents are used to illustrate various nonlinear patterns experienced by the underlined memristive circuit. It is shown that in the absence of the disturbance term, the i - vcharacteristic of the memristor is perfectly symmetric which induces typical behaviours such as coexisting symmetric bifurcation and bubbles, spontaneous symmetry-breaking, symmetry recovering, and coexistence of several pairs of mutually symmetric attractors. With the perturbation term, the symmetry of the oscillator is destroyed resulting in more complex nonlinear phenomena such as coexisting asymmetric bubbles of bifurcation, critical transitions, and multiple coexisting (i.e. up to five) asymmetric attractors. Also, PSpice simulation studies confirm well the results of theoretical predictions.

Automated summary

The paper examines the dynamics of a memristive circuit with broken symmetry, using phase portraits, bifurcations, basins of attraction, and Lyapunov exponents to illustrate various nonlinear patterns. It is shown that perturbing the symmetry of the oscillator leads to more complex nonlinear phenomena, such as coexisting asymmetric bubbles of bifurcation and multiple asymmetric attractors, with PSpice simulation studies confirming the theoretical predictions.