| Memristor is a non-linear element with memory function,the non-linear characteristics of memristor make it possible to yield more complex dynamics when memristor is coupled to a chaotic system.In addition,memristor is the most ideal device for constructing artificial nerve synapses due to the memory characteristics of memristor,which also brings memristor into the study on neural networks.Neural networks with memristor are closer to biological neural networks in terms of structure and behavior,and can exhibit complex discharge phenomena,such as chaos and bifurcation.Different memristor models also make it possible for memristive chaotic systems or memristive neural networks to generate diverse dynamic behaviors.At present,employing memristors to construct memristive systems with complex dynamics is beneficial to revealing the mechanism of certain physiological and pathological processes in organisms and generating chaotic signals used in engineering,which has been a hot research.Based on this,this paper proposes a series of memristive systems,including a memristive circuit system,a memristive neuron model,memristive neural networks and so on.The main contents of the paper are as follows:(1)Based on the generalized Lorenz systems,a memristive chaotic system is proposed,and its dynamic behaviors are simply analysed.In addition,a simple circuit with two memristor is also constructed.The multistability in the circuit is numerically analyzed,and the theoretical results are verified by an analog circuit simulation.(2)A new ideal memristor model with cosine function is designed.The dynamic behaviors of Hindmarsh–Rose(HR)neuron model under the electromagnetic radiation excited by the memristor are studied in detail.Numerical analysis reveals the existence of hidden extreme multistability,growth of attractor and so on.The memristive HR neuron model is realized by an analog circuit simulation.(3)An ideal memristor model with hyperbolic tangent function series is proposed.A memristive Hopfield neural network is constructed by using the designed memristor as a synapse in a Hopfield neural network,and the network can generate multi-double-scroll chaotic attractors.The analysis shows that the network system has complex dynamic characteristics,such as controllable multistability,adjustable memductance function and amplitude control.Based on PSIM software,some typical dynamics in the network are implemented.(4)The proposed ideal memristor model with hyperbolic tangent function serises is modified.Several modified memristors are introduced into a Hopfield neural network in the form of neural synapses,constructing three memristive Hopfield neural networks with different number of memristive synapses.The grid multi-double-scroll chaotic attractors generated by the memristive Hopfield neural networks and other dynamical characteristics are studied in detail by the numerical analysis method.Based on microcontroller,the grid multi-double-scroll attractors are implemented physically. |
