A simple inductor-free memristive circuit with three line equilibria

In this work, a novel inductor-free fourth-order two-memristor-based chaotic circuit is proposed. This new circuit is developed from a current feedback op amp-based sinusoidal oscillator through replacing a linear resistor with a memristor and adding another different parallel memristor to the cascaded memristor–capacitor net. The proposed circuit can perform chaotic, fixed point, and period behaviors. The most striking feature is that this system has three line equilibria and exhibits the extreme multistability phenomenon of the coexisting infinitely many attractors. Specially, amplitude death behavior and transient transition behavior can also be found in the proposed system. By using standard nonlinear analysis tools including system dissipation, equilibrium point stability, phase portrait, Lyapunov exponent spectrum, and bifurcation diagram, the fundamental dynamical characteristics of the circuit are investigated in detail. Moreover, a MULTISIM circuit is designed to verify the numerical simulations.