Combinatorics

Physics

Nonlinear system

Attractor

Offset (computer science)

Topology (electrical circuits)

Bifurcation

Mathematics

Phase portrait

Memristor

Mathematical analysis

Artificial intelligence

Eigenvalues and eigenvectors

Control (management)

Programming language

Computer science

Hopfield network

Quantum mechanics

Differential equation

Equilibrium point

Control theory (sociology)

Artificial neural network

IEEE Transactions on Industrial Electronics

Memristor synapse with activated synaptic plasticity can be taken as an adaptive connection synaptic weight. To demonstrate its kinetic effects, in this article, we present an improved Hopfield neural network with two memristive self-connection synaptic weights. The two-memristor-based Hopfield neural network (TM-HNN) has a plane equilibrium set related to two-memristor initial conditions and its stability distributions are analyzed by two nonzero roots of the eigenvalue polynomial. Afterward, the parameter-related bifurcation behaviors are investigated using bifurcation plots and phase portraits. Emphatically, the kinetic effects of memristor synapses are demonstrated by taking the memristor initial conditions as two invariant measures. The theoretical and numerical results show that the TM-HNN can exhibit the wondrous offset-control plane coexisting behaviors and its plane coexisting attractors can be controlled by switching the two-memristor initial conditions. Besides, a digital hardware device is developed and the offset-control plane coexisting attractors are experimentally reproduced to verify the numerical ones.

Offset-Control Plane Coexisting Behaviors in Two-Memristor-Based Hopfield Neural Network