This paper investigates a Hopfield neural network (HNN) under the simulation of external electromagnetic radiation and dual bias currents, in which the fluctuation of magnetic flux across the neuron membrane is used to emulate the influence of electromagnetic radiation. Utilizing conventional analytical methods, the basic properties of the proposed Hopfield neural network are discussed. Due to the addition of electromagnetic radiation and dual bias currents, the Hopfield neural network shows high sensitivity to system parameters and initial conditions. The proposed Hopfield neural network possesses multistability with periodic attractor, quasi-periodic attractor, chaotic attractor and transient chaotic attractor, and all of the attractors are hidden attractors because there is no equilibrium point in the system. In particular, when the neuron membrane magnetic flux is different, the system can present transient chaos with different chaotic times. More interestingly, with the change of system parameters, the proposed Hopfield neural network can exhibit parallel bifurcation behaviors. Finally, the Multisim simulation and hardware experiment results based on discrete electronic components are conducted to support the numerical ones.These results could give useful information to the study of nonlinear dynamic characteristics of the Hopfield neural network.

Due to the potential difference between two neurons and that between the inner and outer membranes of an individual neuron, the neural network is always exposed to complex electromagnetic environments. In this paper, we utilize a hyperbolic-type memristor and a quadratic nonlinear memristor to emulate the effects of electromagnetic induction and electromagnetic radiation on a simple Hopfield neural network (HNN), respectively. The investigations show that the system possesses an origin equilibrium point, which is always unstable. Numerical results uncover that the HNN can present complex dynamic behaviors, evolving from regular motions to chaotic motions and finally to regular motions, as the memristors’ coupling strength changes. In particular, coexisting bifurcations will appear with respect to synaptic weights, which means bi-stable patterns. In addition, some physical results obtained from breadboard experiments confirm Matlab analyses and Multisim simulations.

By introducing flux-controlled memristor and linear feedback term into the three-dimensional (3D) chaotic system, and using the state feedback control method to increase dimension, a novel variablewing 5D memristive hyperchaotic system has been proposed in this paper. The proposed memristive hyperchaotic system has a line equilibrium point whose position is directly determined by the control parameter. The remarkable feature of the system is that the influence of positive feedback memristor and negative feedback memristor on the system and their similarities and differences are considered. Meanwhile, by analyzing the complex dynamic behavior of the system under different control parameters and initial values, it can be found that the proposed memristive hyperchaotic system shows many interesting phenomena including hidden extreme multistability, transient chaotic transition behavior and variable-wing characteristics. Finally, the hardware electronic circuit of the memristive hyperchaotic system is designed. The hardware experimental results are highly consistent with the numerical simulation ones, which demonstrate the physical realizability of the proposed system.

This paper investigates a Hopfield neural network (HNN) under the simulation of external electromagnetic radiation and dual bias currents, in which the fluctuation of magnetic flux across the neuron membrane is used to emulate the influence of electromagnetic radiation. Utilizing conventional analytical methods, the basic properties of the proposed Hopfield neural network are discussed. Due to the addition of electromagnetic radiation and dual bias currents, the Hopfield neural network shows high sensitivity to system parameters and initial conditions. The proposed Hopfield neural network possesses multistability with periodic attractor, quasi-periodic attractor, chaotic attractor and transient chaotic attractor, and all of the attractors are hidden attractors because there is no equilibrium point in the system. In particular, when the neuron membrane magnetic flux is different, the system can present transient chaos with different chaotic times. More interestingly, with the change of system parameters, the proposed Hopfield neural network can exhibit parallel bifurcation behaviors. Finally, the Multisim simulation and hardware experiment results based on discrete electronic components are conducted to support the numerical ones. These results could give useful information to the study of nonlinear dynamic characteristics of the Hopfield neural network.

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