Study Of Chaotic Ant Swarm Optimizatition Algorithm And H-R Neural Network Dynamics

Synchronized neural behavior is an important focus of research in neural networks dynamics. A lot of work has been done in this area, such as on the effects of network topology on synchronization and the relations between synchronization patterns and coupling strength or connection time delay. In this article, we use a chaotic ant swarm(CAS) optimization algorithm to compute the optimal coupling relations of neural networks based on Hindmarsh-Rose(H-R) model neurons. This article contains two parts: the study of our optimization algorithm and the calculation of optimal coupling relations in H-R neural networks that can achieve an optimal synchronization state.The chaotic ant swarm optimization algorithm makes use of a model of “swarm intelligence” and, as with similar optimization algorithms, the ending state is not easy to accurately set or predict. In Chapter 2, we design an effective ending condition according to the characteristics of CAS, making use of several test functions to verify the validity of the conditions. Numerical experiments show that the proposed ending conditions can achieve the optimal solution by repeated application of the search algorithm. Our research results were published in Acta Physica Sinica, Vol. 62, Issue 17.In Chapter 3, parameter estimation is obtained from the partial series of chaotic systems with the CAS, in order to better understand the chaotic system. This article proposes a simple and practical chaotic secure communication method based on the parameter estimation from the obtained partial trajectory series. Numerical simulation validated the feasibility of our chaotic system partial series parameter estimation and the chaotic secure communications method. Numerical experiments show that the synchronization between the system obtained from parameter identification and the original system cannot be maintained for long times. In our communication method, the series of chaotic systems that can be accurately obtained is not only for identification but also for error correction in the communication process. When the two systems have large deviation, they require parameter identification again to maintain synchronization, so the communication method requires several parameter estimation steps. This results in secure communication that can be maintained with long time. The research results were published in Acta Physica Sinica, Vol. 63, Issue 1.In Chapter 4, we transform the problem of optimal coupling relations in H-R neural networks into an optimization problem, namely to find an optimal coupling matrix that can make the neural networks achieve the complete synchronization state. Then, we use the CAS algorithm to resolve the optimization problem and thus derive the optimal coupling matrix. Numerical simulation shows that the neural networks with optimized coupling relations can rapidly achieve synchronization. Finally, the article discusses the next steps of future research development for our approach.