A Multi Frequency Sinusoidal Chaotic Neural Network And Its Complex Dynamics Analysis And Applications

The chaotic neural network is a highly nonlinear dynamic system,which can realize a series of complex dynamic behaviors,optimize global search and neural computation,and generate pseudo-random sequences for information encryption.Because the biological neural network is a strongly nonlinear system,so it can appear chaotic phenomenon.In order to achieve this behavior in the artificial neural network,the nonlinear function is usually used as its activation function.However,traditional activation functions don't have biological mechanisms.In this paper,a non-monotone activation function based on the multi frequency-frequency conversion sinusoidal function and a piecewise function is proposed to make the neural network more consistent with the biological characteristics,based on the superposition theory of sinusoidal signals with different frequencies of brain waves.Two chaotic neural network models are designed,one is MFCS chaotic cellular neural network model,the other is MFCS chaotic Hopfield neural network model,and audio encryption is carried out by using MFCS chaotic cellular neural network model.The main work of this paper is as follows:(1)Based on the research of brain wave and neural network activation function,an activation function with biological mechanism is designed,which can simulate the frequency and amplitude of EEG signals by adjusting parameters,and simulate the state of multiple EEG signals acting at the same time.The activation function fits human brain structure more closely.In this paper,we used Matlab simulation software to simulate EEG signal based on the activation function.The results proved that the activation function is not prone to gradient disappearance and can simulate the EEG signals with different frequency and amplitude and their effects on the neural network well.(2)In order to explore the effect of multi-frequency sinusoidal activation function with biological mechanism on chaotic neural network.Based on the chaotic neural network theory,the MFCS chaotic Hopfield neural network model is proposed by introducing the multi-frequency sinusoidal activation function into the Hopfield neural network.The complexity of MFCS chaotic Hopfield neural network model is explored by Lyapunov exponent spectrum,SE and C0 graph.At the same time,we used attractor,bifurcation graph and Lyapunov exponent spectrum to analyze the chaotic dynamics characteristics.The experiment shows that the model has high complexity and very complex chaotic dynamics.(3)In order to verify the complex chaotic dynamics behavior of the multi-frequency sine function in other chaotic neural networks,we constructed MFCS chaotic cellular neural network model,by introducing multi-frequency sine function into the cellular neural network.Using attractor,bifurcation graph,Lyapunov index and SE and C0 graph,the complexity and chaotic dynamics of the model are analyzed.The experiment result shows that multi-frequency sinusoidal activation function can also generate rich chaotic dynamic behaviors in cellular neural networks,which lays a solid foundation for the application of chaotic neural networks in secure communication.(4)The application of chaotic neural network model is studied in secure communication.Based on chaotic cellular neural network sequence,combining the artificial key,the audio encryption key generated by chaotic sequence,an improved encryption algorithm is designed.The algorithm improves the utilization of chaotic sequence,improves user experience and has high security.Finally,the simulation experiment is carried out to realize the encryption and decryption of audio,which proves the effectiveness and security of the algorithm.