Multi-Scroll Memristive Neuron Network Model Design And Its Application In Image Encryption

Neurobiological experiments show that the brain with a large number of neurons and neuron networks is a highly complex nonlinear system.As a component of the brain’s nervous system,the most basic task of neurons is to convert the received external stimuli into neural coded information,process the information,and then make corresponding responses,which are transmitted to the next neuron via nerve synapses.The complex electrical activities of a single neuron itself and multiple neuron networks are closely related to the unique memory,thinking and learning abilities of the brain,and play a pivotal role in the transmission and coding of neural information.In addition,under the influence of external electromagnetic radiation stimulation,abnormal electrical firings will occur between neurons,which may lead to certain neurological diseases.Therefore,studying the relevant mechanisms of neuronal firing activities not only helps to understand the pathogenesis of neurological diseases,but also helps to further understand how the brain encodes and decodes external information.This is conducive to the design of neuromorphic systems with brain-like functions and promotes the development of neuroscience.However,traditional neuron and neuron network models,such as the Hodgkin-Huxley model,have complex structures,large parameters,high computational complexity,single firing mode,simple dynamics,and no complex chaotic behaviors.It cannot truly reflect the rich discharge dynamics of biological neurons,which brings difficulties to circuit design and implementation,and is not conducive to its application in the field of artificial intelligence.In response to the above problems,this dissertation uses memristive devices,combines chaos and circuit theory knowledge,and considers factors such as external electromagnetic field stimulation to design a series of neurons and neuron network models with simple structures,rich dynamic characteristics and easy-to-implement circuits.The main work and innovative research results are as follows:Based on the memristor theory,novel local passive ideal and non-ideal piecewise nonlinear flux-controlled memristor models are designed respectively.This kind of memristor model has the characteristics of flexible and adjustable memristive value,and can be used to generate any number of multi-single-scroll and multi-double-scroll chaotic attractors.Furthermore,according to the local active theory and the principle of non-volatility,a locally active non-volatile memristor model with multi-stable properties is designed.Finally,the corresponding equivalent circuit model is designed.The circuit experiment results demonstrate the validity and feasibility of the designed memristor model.It lays the foundation for the subsequent building of neural synapse modules,description of external electromagnetic radiation effects,and design of multi-scroll memristive neurons and neuron network models.By adopting an ideal piecewise nonlinear flux-controlled memristor model to describe the effect of external electromagnetic radiation,a novel no-equilibrium multi-single-scroll memristive Hindmarsh-Rose(HR)neuron model with electromagnetic radiation effect is designed.Compared with other memristive HR neuron models,this model can generate odd-even controllable multi-scroll hidden attractors with complex topologies,and the scroll number of the multi-scroll hidden attractors is also related to the strength memristive electromagnetic radiation stimulation.The theoretical analysis and numerical simulation are proved by hardware circuit experiments.On this basis,a pseudo-random number generator and an image encryption scheme are designed.The performance analysis results show that the model has good randomness and high security,and is suitable for image encryption applications.By introducing the non-ideal piecewise nonlinear flux-controlled memristor model into the Hopfield neuron network(HNN),a novel multi-double-scroll memristive synaptic HNN model is constructed.The model exhibits complex dynamical behaviors such as odd-even controllable double scrolls,amplitude control,initial offset-boosted coexisting dynamics,homogeneous multistability,etc.Then,the simulated electronic circuit of the model is designed,and the circuit simulation verifies the numerical simulation results.Finally,the random performance of the initial offset-boosted coexisting double-scroll attractors is tested using the NIST test suite and an image encryption scheme is designed.In contrast,the network model has a large key space and strong key sensitivity,which further illustrates its high security in image encryption applications.Based on the ideal piecewise nonlinear flux-controlled memristor model and the locally active non-volatile memristor model,a grid multi-scroll memristive autapse-based single neuron model with external electromagnetic radiation effect is designed.The flux-controlled memristor model is used to describe the effect of external electromagnetic radiation,and the locally active non-volatile memristor model is used to simulate the neuron self-synaptic.Numerical analysis shows that the model can not only generate grid multi-scroll chaotic attractors but also produce abundant firing patterns.The simulation circuit of the model is designed and implemented,and the numerical simulation results are verified by hardware experiments.The experimental results show that the memristive neuron circuit can generate various types of firing patterns that are close to actual biological neurons.The new multi-scroll memristive neuron and neuron network models designed in this dissertation can generate complex chaotic dynamic characteristics and rich firing patterns,can better simulate the dynamic characteristics of the brain,and provide theoretical basis for actual physiological experiments and model reference.It also provides new methods and ideas for the development of brain-inspired intelligent systems,which can further promote the development of artificial intelligence.