A Simple Third-Order Memristive Band Pass Filter Chaotic Circuit

This brief presents a simple third-order inductor-free memristive chaotic circuit, which is derived from a second-order active band pass filter (BPF) by replacing a resistor with an improved memristor and has only three op-amps, two multipliers, three capacitors, and six resistors. The circuit has three unstable saddle-foci and exhibits complex dynamical behaviors, including period, chaos, period doubling bifurcation, coexisting bifurcation modes, and constant Lyapunov exponents (CLEs). Especially, the property of CLEs leads to that the amplitudes of the chaotic signals are linearly controlled by a potentiometer without changing system's essences. Moreover, hardware circuit using less discrete components is fabricated and experimental verifications are performed, from which the existence of chaos is validated. Compared with other memristive chaotic circuits reported before, the proposed memristive BPF chaotic circuit is inductor-free and topologically simplified, which is only third-order, and much simpler and more intuitive in practical realization.