On The Dynamical Behaviors Of Neural Networks System On Time Scales

The combination of theory of time scale and neural networks are new fields in ex-plorations of motions, mathematically describe continuous and discrete hybrid processesand hence is the optimal way forward for accurate and malleable mathematical model,and then, it is very meaningful to study the stability of hybrid systems. In this paper,by using the theory of time scale, global exponential stability of delayed BAM neuralnetworks with impulses on time scales and stability and existence of periodic solutions todelayed BAM neural networks with impulses on time scales are studied, respectively. Themain contents in this paper can be summarized as follows:The first section is introduction, in which we present research background, purposeand significance of impulses and neural networks of impulses control, and then the researchstatus quo and results of neural networks with impulses control on time scales are given.Finally, the organization of this paper is also presented.The BAM neural networks with impulses control on time scales are introduced inSection 2.In Section 3, global exponential stability of delayed BAM neural networks with im-pulses on time scales is discussed. Some sufficient conditions ensuring the global expo-nential stability and exponential stability of dynamic system are obtained by designinga linear impulsive controller and Lyapunov function based on time scales. Finally, somenumerical examples and simulations are presented to show the feasibility and effectivenessof the proposed methods.Global exponential stability of periodic solutions to delayed BAM neural networkswith impulses on time scales is discussed. The linear impulsive controller and Lyapunovfunction are investigated in Section 4, some new and su?cient conditions ensuring theglobally exponential stability of periodic solutions to delayed BAM neural networks arederived. Finally, some numerical simulations are presented to verify the obtained results. In section 5, Anti-periodic solutions for high-order Cohen-Grossberg neural networksis discussed, and some su?cient criteria to guarantee the exponential stability of anti-periodic solutions are derived. The results obtained in this section are new and usefulverified through simple algebraic methods.