| The brain is a highly complex nonlinear dynamic system,which is one of the most complex systems in the universe with multi-level complex morphological structures and a variety of information network connection and processing modes.Gradually understanding and solving the mystery of brain function is the most challenging problem in multidisciplinary frontier field,and also the arduous mission of human scientific development.Neurons are the basic units of brain function and structure,the nonlinear dynamics theory opens up a new way to explore the neurons activities and gradually reveal the laws of the brain magical activities.For a long time,the study of neuron activity by using nonlinear dynamics theory mainly focuses on classical neuron mathematical models,such as HH neuron model,ML neuron model and HR neuron model.In order to further study the more realistic nonlinear activity of neurons,it is necessary to consider the electromagnetic induction effect,neuron signal transmission delay,and so on.Studying on the neuron model with electromagnetic induction effect and distributed delay can reflect more important theoretical significance and practical application value.In the thesis,from the perspective of nonlinear dynamics,the constitutive mechanism and nonlinear dynamic characteristics of the electromagnetic induction neuron model and the neuron model with distributed delay are analyzed,and their applications in color image encryption are preliminarily explored.At the same time,in order to achieve more reliable and stable information transmission of encrypted images under high-speed mobile environment,an improved joint information transmission mechanism is proposed,and the performance is further compared with the traditional information transmission mechanism and the optimized information transmission mechanism.The main work of this thesis has the following several aspects:(1)On the basis of the m-HR neuron model,considering the influence of electromagnetic induction on the neuron and introducing the flux-controlled memristor,the feedback modulation of the magnetic flux variable on the membrane potential is realized and the improved m-HR neuron model is obtained.Then,the nonlinear dynamics theory is used to study the local stability,global bifurcation and other nonlinear characteristics of the improved m-HR neuron model under electromagnetic induction.The double parameters bifurcation analysis and the maximum Lyapunov exponent diagram are used to prove that the improved m-HR neuron model exhibits the classic comb-like chaotic structure and periodic bifurcation mode in the multi-parameter space.At the same time,based on the optimization and improvement of the traditional Hamiltonian controller,an intermittent feedback controller is proposed,which can effectively adjust the electrical mode of periodic cluster.And so higher periodic cluster discharge activity is obtained and chaotic electrical behavior can be suppressed to make it appear periodic oscillation mode.In order to compare the advantages and disadvantages of the feedback modulation effect of the intermittent controller and the continuous controller,the numerical simulation is used to verify that effect of the intermittent feedback controller is obviously better than that of the traditional continuous feedback controller,and the intermittent controller has a wider range of adjustable parameters and less energy loss.Finally,the unknown parameters of the improved m-HR neuron model are identified,and the driving system,response system and error system are constructed by using the active control method.The Lyapunov function is constructed to realize the synchronization and parameter identification of the improved m-HR neuron system.Numerical simulation results are consistent with the theory,and the effectiveness of the synchronization scheme is verified.(2)Based on the existing neuron model under electromagnetic induction,discrete and distributed time delays are introduced to analyze the stability,local bifurcation,global bifurcation and chaos of biological systems.The nonlinear dynamic behavior of discrete delay and distributed delay neuron models is discussed,especially for stability and Hopf bifurcation.The relationship between strong kernel function and weak kernel function in distributed delay is transformed mathematically to obtain a neuron model with discrete delay only.Taking the discrete delay as the bifurcation parameter,the influence of distributed delays with different kernel functions on the stability of the system is analyzed by using the center manifold theorem.It is found that Hopf bifurcation occurs earlier in the strong kernel distributed delay model than in the weak kernel distribution.The numerical simulation is used to verify,and the two-parameter bifurcation diagrams under different time delays are given.The correctness of the conclusion is verified,and further illustrate that if the kernel function needs to be considered to control the distributed delay system in practical application,the weak kernel function or the strong kernel function can be selected according to the conclusion.(3)Through the nonlinear dynamic analysis of the neuron model in Chapter 3and Chapter 4,it can be found that both the m-HR neuron model under the influence of electromagnetic induction and the flux neuron model with distributed delay have very rich conversion modes.There is a large range that can keep a chaotic state for each parameter in the system,indicating that the system has enough randomness and is more suitable for image encryption.A color image encryption algorithm is designed based on m-HR neurons with electromagnetic induction effect,HR neuron system with distributed delay of strong and weak nuclei and DNA sequence operation respectively.The DNA sequence operation is used to spread the scrambled image to obtain the final encrypted image.At the same time,the security analysis is carried out and the results show that the design of encryption algorithm can effectively encrypt the image with high security and robustness,and can resist various common attacks.(4)On the premise that image security technology ensures information security,considering the transmission of image information in high-speed scenes,analyzing the research status of current IEEE 802.11 and considering the mismatch with high-speed scenes,a data access transmission mechanism of joint retransmission technology is designed to improve the efficiency in the information transmission.In order to verify the effectiveness of the proposed mechanism,the two-dimensional Markov models of the traditional mechanism and the improved mechanism in the high-speed scenario are established respectively,and the analytical expressions of the system performance indicators such as channel transmission probability,average backoff times,average backoff delay,system total delay and throughput are obtained by using the queuing theory.At the same time,the system parameters are set to conduct numerical simulation comparison between the two mechanisms.The results show that,in the high-speed scenarios,compared with the traditional mechanism,the mechanism will greatly improve the system performance.And the faster the moving speed is,the more obvious the mechanism superiority is. |
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