Abstract
A new hyperbolic-type memristor emulator is presented and its frequency-dependent pinched hysteresis loops are analyzed by numerical simulations and confirmed by hardware experiments. Based on the emulator, a novel hyperbolic-type memristor based 3-neuron Hopfield neural network (HNN) is proposed, which is achieved through substituting one coupling-connection weight with a memristive synaptic weight. It is numerically shown that the memristive HNN has a dynamical transition from chaotic, to periodic, and further to stable point behaviors with the variations of the memristor inner parameter, implying the stabilization effect of the hyperbolic-type memristor on the chaotic HNN. Of particular interest, it should be highly stressed that for different memristor inner parameters, different coexisting behaviors of asymmetric attractors are emerged under different initial conditions, leading to the existence of multistable oscillation states in the memristive HNN. Furthermore, by using commercial discrete components, a nonlinear circuit is designed and PSPICE circuit simulations and hardware experiments are performed. The results simulated and captured from the realization circuit are consistent with numerical simulations, which well verify the facticity of coexisting asymmetric attractors' behaviors.
Highlights
The neurons regarded as the fundamental component unit of brain can generate intricate dynamical behaviors (Korn and Faure, 2003; Ma and Tang, 2017) and the constructing Hopfield neural network (HNN) (Hopfield, 1984) is a significant model in artificial neurology
We present a hyperbolic-type memristor based 3-neuron Hopfield neural network (HNN) on the basis of the reference (Zheng et al, 2010), which can show the stabilization effect of the hyperbolic-type memristor on the chaotic HNN, resulting in a dynamical transition from chaotic, to periodic, and further to stable point behaviors with the variations of the memristor inner parameter
For different memristor inner parameters, different coexisting behaviors of asymmetric attractors are emerged under different initial conditions, which are availably validated by PSPICE circuit simulations and hardware experiments
Summary
The neurons regarded as the fundamental component unit of brain can generate intricate dynamical behaviors (Korn and Faure, 2003; Ma and Tang, 2017) and the constructing Hopfield neural network (HNN) (Hopfield, 1984) is a significant model in artificial neurology. Double-scroll chaotic attractor Right-chaotic spiral attractor and double-scroll chaotic attractor Right-period-1 limit cycle and left-chaotic spiral attractor Right-period-1 limit cycle and left-period-4 limit cycle Right-stable point attractor and left-period-2 limit cycle Right-stable point attractor and left-period-2 limit cycle Right-stable point attractor and left-period-3 limit cycle the memristor inner parameter b is adjusted in the region of [0, 0.6], the coexisting behaviors of asymmetric attractors in the hyperbolic-type memristor based HNN can be revealed by bifurcation diagrams, Lyapunov exponent spectra, and phase portraits.
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