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.

In this paper, to be more precise in modeling the real epidemic spread, an SEIR model with delay describing the fixed latent period is studied on scale-free networks. The basic reproduction number, which serves as a critical threshold of epidemic spread, is calculated. The formula for the basic reproduction number shows that adding delay decreases the basic reproduction number. By constructing appropriate Lyapunov functions, the global stability of disease-free and endemic equilibria is investigated. Finally, numerical simulations are performed to illustrate the effect of network structures and model parameters on the basic reproduction numbers and disease spreading processes.