Coexisting Behaviors of Asymmetric Attractors in Hyperbolic-Type Memristor based Hopfield Neural Network

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.

Takacs Model of Hysteresis in Mathematical Modeling of Memristors

“…Hyperbolic-type memristor with memductance expressed via the hyperbolic tangent function of state variable is proposed in [51]. Although not explicitly reported, HL appears in the memductance-flux plane of this type of memristor.…”

Memristor‐Based Canonical Chua’s Circuit: Extreme Multistability in Voltage‐Current Domain and Its Controllability in Flux‐Charge Domain

“…It should be mentioned that just like the ideal flux/ voltage-controlled memristor-based chaotic circuits [4][5][6][7][8][9], the proposed memristor-based canonical Chua's circuit has a line equilibrium point with complicated stability distributions already depicted in Figures 2-4, whereas most of conventionally nonlinear dynamical systems with no equilibrium point [10], with only several determined equilibrium points [15][16][17][18][19][20][21], or with curves of equilibrium points [41][42][43] have relatively simple stability distributions with some divinable nonlinear dynamical behaviors.…”

“…Generally, multistability is confirmed in hardware experiments by randomly switching on and off experimental circuit supplies [9,[15][16][17][18][19][20][21] or by MATLAB numerical or PSPICE/PSIM circuit simulations [4][5][6][7][8][22][23][24][25][26][27][28]. Consequently, to direct the nonlinear dynamical circuit or system to a desired oscillating mode, an effective control approach should be proposed [12].…”

Investigation of Cortical Signal Propagation and the Resulting Spatiotemporal Patterns in Memristor‐Based Neuronal Network

“…In our work, the proposed Hopfield network is achieved by replacing resistive connection with hyperbolic-type memristor, which is discussed in detail in [35]. The set of parameters are = 3, = 1, = 1 ( = (1 : 3)).…”

“…Hopfield neural model is defined as a graded response model [34]. This model has been successful in representing different dynamical behaviors including chaotic behaviors [35,36] having to do with nonlinear demonstrations of the brain performance.…”