Abstract
By replacing a series resistor in active band pass filter (BPF) with an improved memristive diode bridge emulator, a third-order memristive BPF chaotic circuit is presented. The improved memristive diode bridge emulator without grounded limitation is equivalently achieved by a diode bridge cascaded with only one inductor, whose fingerprints of pinched hysteresis loop are examined by numerical simulations and hardware experiments. The memristive BPF chaotic circuit has only one zero unstable saddle point but causes complex dynamical behaviors including period, chaos, period doubling bifurcation, and coexisting bifurcation modes. Specially, it should be highly significant that two kinds of bifurcation routes are displayed under different initial conditions and the coexistence of three different topological attractors is found in a narrow parameter range. Moreover, hardware circuit using discrete components is fabricated and experimental measurements are performed, upon which the numerical simulations are validated. Notably, the proposed memristive BPF chaotic circuit is only third-order and has simple topological structure.
Highlights
Due to the unique nonlinear characteristics of memristors [1], an explosive growth study of memristor based circuits has been boosted up in the past years [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]
Inspired by the advantages of those methodologies in building chaotic circuit, a novel and simple memristive band pass filter (BPF) chaotic circuit with complex dynamical behaviors is constructed from a second-order active BPF by replacing a series resistor with our proposed memristive diode bridge emulator
A third-order memristive BPF chaotic circuit is presented, which is constructed by replacing a resistor in second-order active BPF with an improved memristive diode bridge emulator
Summary
Due to the unique nonlinear characteristics of memristors [1], an explosive growth study of memristor based circuits has been boosted up in the past years [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16]. Numerous memristive dynamical circuits have been reported by introducing memristor into classical linear or nonlinear dynamical circuits [4, 5, 9, 13, 14, 16, 20,21,22,23], from which complex dynamical behaviors, such as chaotic behaviors [4, 5, 20, 21], coexisting multiple attractors [9, 13], selfexcited and hidden attractors [14, 22, 23], and chaotic and periodic bursting [16], have been revealed and analyzed by theoretical analyses, numerical simulations, and experimental measurements. It is very attractive to seek for a simple memristive chaotic circuit that has the striking dynamical behavior of coexisting multiple attractors. Inspired by the advantages of those methodologies in building chaotic circuit, a novel and simple memristive BPF chaotic circuit with complex dynamical behaviors is constructed from a second-order active BPF by replacing a series resistor with our proposed memristive diode bridge emulator.
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