The Existence And Synchronization Of Impulses Neural Networks

Neural network is nonlinear dynamical system that has a highly complex. Neural network hasabounding dynamics action and stronger mathematics theory basis, which has highly theatrical valueand widely application prospect. Neural network attracts many scholars in the diferent fields such asmathematics, information, automation, engineering and economy.Impulse and time delay phenomenon exist everywhere in practical problems of all kinds of modernscientific fields. The most outstanding feature of them is that they are able to consider the influence ofmomentary disturbance phenomenon and time delay. And they are able to reflect the changeable lawmuch deeper and more accurate. They already become the hot problem in nonlinear science research.The paper applies Mawhin’s continuation theorem of the coincidence degree, bifurcation theory andnumerical simulation to study the dynamics character of the traditional neural network model, afterwhich is imposed impulse and time delay. The paper finds out that impulse and time delay have a greatinfluence to the stability and periodicity of neural network, especially, there is Gui attractor under theadequate impulse.The paper also study the problem of impulse synchronization between two neural network systems,which is the key technology that neural network applies in the chaotic science communication. The paperis deviled into five parts.The first chapter, generally states the significance and application of neural network research, andintroduce impulse diferential equation, Lyapunov function, the concept of diferential equation stabilityand the chaotic strange attractor.In chapter two, we increase the influence of impulse and time delay for the traditional Lotka-Volterrareflex neural network, such improvement is necessary,when neural network applies in practical problems.For example, when neural network applies in chaotic secret communication, the signal transfer will bringthe influence of time delay, and the limit of tape span needs impulse synchronization. Therefore, we studythe dynamics character of Lotka-Volterra reflex neural network, which had impulse and delays influenceand we abstain the sufcient conditions of the existence of periodic solution.In chapter three, we apply topology contact ratio theory and Lyapunov function to study the higherorder which has impulse, delays of Hopfield neural network periodic solution existence. We also applythe computer value imitation to study its chaotic.In chapter four, the paper study the impulse neural network of neural network model and give astrategy of neural network synchronization which is based on impulse control, and abstain the sufcientcondition of synchronization. At last, applying computer simulative results verifies the feasibility andefectiveness.In chapter five, the paper summarizes the study of the paper and looks forward to the continuingresearch.