An autonomous memristive circuit is implemented by an active third-order generalized memristor. The mathematical model is established and the stability of the equilibrium point and divergence are analyzed. Lyapunov exponents and bifurcation analysis demonstrate the complex dynamical behaviors of the system. As an internal parameter of voltage controlled memristor is changed, the system changes from bursting chaos to general chaos, which includes chaotic bursting attractor and periodic bursting attractor. This system produces periodic bursting similar to the clusters discharge of biological neurons. Interestingly, the system differs from the single helical clusters discharge of neurons. The bifurcation mechanism of the periodic bursting behavior is explored by constructing equilibrium trajectories of the fast-scale subsystem to verify the Fold bifurcation and to establish the Hopf bifurcation sets. Finally, it is shown that a circuit experiment based on Multisim is consistent with the theoretical analysis and numerical simulations, which proves the feasibility of the real circuit.
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