Controllability For Stochastic Age-Dependent Population System And BAM Neural Networks

In order to further reveal the rule of developing in biology, stochastic differential equations can be as tools to study the important issues in biology. It is obtained that differential equations can better de-scribe the practical situation in the research of materials which have memory process, hereditary property or heterogeneous characteristics. However, for any of the actual system, it can be affected by the un-certain factors, meanwhile, the applications of syetems depend on dynamical features. The stochastic age-structured population model and bidirectional associative memory (BAM) neural networks which are the basic model of this paper, the system’s controllability are discussed. This paper mainly discusses the following three parts:Under the equation satisfy boundedness condition(which is weaker than linear growth condi-tion)together with Lipschitz condition, we consider a class of stochastic fuzzy age-structured population system with diffusion. It can apply the method of successive approximation by constructing Picard it-eration sequence to discuss the existence and uniqueness of solutions to stochastic fuzzy age-structured population system with diffusion. At last, an estimation of error of approximate solution is presented.We introduce the approximate controllability of a class of fractional stochastic age-dependent popu-lation dynamic system. Using fixed point principle, fractional calculations, basic theory of stochastic dif-ferential equation, the new sufficient conditions for weak solution of fractional stochastic age-dependent population system is formulated, and also have given the conditions that the system is a approximate controllability. Finally, an example is provided to show the application of our result.We consider the global dissipativity for stochastic bidirectional associative memory (BAM) networks with time delay. By use of Lyapunov functions, Jensen’s inequality, It? formula and some analytic tech-niques, the sufficient condition, which is for the global dissipativity in the mean square of such stochastic bidirectional associative memory (BAM) neural networks, is obtained in linear matrix inequality (LMI) form. It can be easily proved in practice. Finally, the numerical example is provided to demonstrate the effectiveness of our criteria.