| Memristor is a nonlinear component widely used in artificial neural network research due to its non-volatile and biological synaptic properties.Artificial neural networks are inspired by the structure and function of the human brain,and are a critical component of artificial intelligence.Neural networks are composed of neurons coupled through memristors as synapses,exhibiting complex dynamic behavior like human brain signals.The chaotic signals generated by these coupled neural networks with complex dynamic characteristics play an important role in image encryption and transmission.Based on the mathematical models of HR and FN neurons,this paper investigates the complex dynamic behavior of HR-FN coupled neural networks under different types of memristors and coupling methods and implements them in circuits and applies them in image encryption.This paper addresses the problem of traditional memristors having a small range of resistance values,which makes it difficult to construct neural networks with more complex characteristics.A hyperbolic local active memristor model is designed as a synapse,and a neural network based on hyperbolic memristors is constructed to study the different periodic and chaotic behaviors of the network under different coupling strength coefficients and initial conditions,as well as the complex dynamic behavior of periodic-chaos coexistence.In addition,a color image encryption algorithm based on this neural network is designed,and the security of the algorithm is verified through robustness analysis.The design of a neural network based on hyperbolic local active memristors provides ideas for the construction of local active memristors and the development of coupled neural networks in the future.This paper addresses the problem that the current local active memristor model is single and cannot construct neural networks with more complex dynamic behaviors.A hyperbolic local active memristor model with asymmetric hysteresis loops is designed as a synapse,and a neural network based on hyperbolic asymmetric memristors is constructed.Through dynamic analysis methods such as equilibrium point analysis,Lyapunov exponents,bifurcation diagrams,and spectral entropy values,it is verified that the coupled neural network has multiple stability and high complexity chaotic characteristics under the influence of memristors.A new image encryption algorithm is proposed by combining the chaotic sequence generated by the neural network iteration with DNA logic operation.Finally,the encryption algorithm’s strong resistance to attacks is verified through comparative analysis methods such as adjacent pixel correlation analysis,differential attack analysis,and robustness analysis,providing ideas for future research on encryption algorithms based on chaotic neural networks.This paper addresses the problem that hyperbolic memristors are not sensitive to initial conditions and do not meet the input signal sensitivity of biological neural networks.A cosine hyperbolic asymmetric memristor is designed as a synapse,which has hysteresis loops of different shapes under different initial conditions.A neural network based on cosine hyperbolic asymmetric memristors is constructed,and through nonlinear system dynamic analysis methods such as equilibrium point analysis,three-parameter Lyapunov exponent analysis,and attractor analysis,it is found that the neural network has multiple types of coexisting attractors,antimonotonicity,and periodic-chaos coexistence under different parameters and initial values.Secondly,using the chaotic signal generated by the neural network combined with the Fibonacci Q matrix,a new image encryption algorithm is proposed,and its security is verified.The design of cosine hyperbolic asymmetric memristors provides ideas for the study of multi-stable memristors in the future and the construction of neural networks with more complex dynamic behaviors. |
