| This paper is to study the characteristics of the solution of a class of fractional fuzzy neural network systems with generalized piecewise constant argument(GPCA).First,the existence and uniqueness of the solution of the system is studied.By using the method of constructing a similar Picard iterative sequence,the existence of solutions is proved.Then the uniqueness of the solution is proved by using the counter-proof method.Secondly,the existence of a unique equilibrium point of the system is proved by using the contraction mapping principle.On this basis,a translation of the equilibrium point is made for the solution of the system.The problem of studying the behavior of the solution of the original system is transformed into the behavior of the zero solution of the new system,in which case the zero solution of the new system is its equilibrium point.For the fuzzy operation part,an inequality is used to scale the system to be without fuzzy operations;for the GPCA part,a norm estimate is given by inequality,which provides the basis and convenience for the study of the global M-L stability of the solution.By using the second method of Lyapunov,a V function is constructed to prove that the system has global M-L stability under the conditions described in the theorem.Then,the bias in the above system is changed from constant to bounded function.The second method of Lyapunov and the method of inequality are used to prove that the solutions of the system are bounded and M-L stable.After the periodic requirements of the time series of the solution,it is proved that there is no periodic solution in the system,and then the asymptotic periodicity of the system is studied.Finally,it is proved that when the bias of the system satisfies certain conditions,The solution of the system is globally asymptotically stable,and the trajectory of the system converges to a periodic function,that is,the system is globally asymptotically periodic. |
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