In this paper, we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays. In fact, the properties of norms and the contraction ...In this paper, we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays. In fact, the properties of norms and the contraction principle are adjusted to ensure the existence as well as the uniqueness of the pseudo almost periodic solution, which is also its derivative pseudo almost periodic. This results are without resorting to the theory of exponential dichotomy. Furthermore, by employing the suitable Lyapunov function, some delayindependent sufficient conditions are derived for exponential convergence. The main originality lies in the fact that spaces considered in this paper generalize the notion of periodicity and almost periodicity. Lastly, two examples are given to demonstrate the validity of the proposed theoretical results.展开更多
In this paper, we prove the existence and the global exponential stability of the unique weighted pseudo almost-periodic solution of shunting inhibitory cellular neural networks with mixed time-varying delays comprisi...In this paper, we prove the existence and the global exponential stability of the unique weighted pseudo almost-periodic solution of shunting inhibitory cellular neural networks with mixed time-varying delays comprising different discrete and distributed time delays. Some sufficient conditions are given for the existence and the global exponential stability of the weighted pseudo almost-periodic solution by employing fixed point theorem and differential inequality techniques. The results of this paper complement the previously known ones. Finally, an illustrative example is given to demonstrate the effectiveness of our results.展开更多
This paper considers the drive-response synchronization in finite-time and fixed-time of inertial neural networks with time-varying and distributed delays(mixed delays). First, by constructing a proper variable substi...This paper considers the drive-response synchronization in finite-time and fixed-time of inertial neural networks with time-varying and distributed delays(mixed delays). First, by constructing a proper variable substitution, the original inertial neural networks can be rewritten as a first-order differential system. Second, by constructing Lyapunov functions and using differential inequalities,some new and effective criteria are obtained for ensuring the finite-time synchronization. Finally, three numerical examples are also given at the end of this paper to show the effectiveness of the results.展开更多
In this paper,a neutral Hopfield neural network with bidirectional connection is considered.In the first step,by choosing the connection weights as parameters bifurcation,the critical point at which a zero root of mul...In this paper,a neutral Hopfield neural network with bidirectional connection is considered.In the first step,by choosing the connection weights as parameters bifurcation,the critical point at which a zero root of multiplicity two occurs in the characteristic equation associated with the linearized system.In the second step,we studied the zeros of a third degree exponential polynomial in order to make sure that except the double zero root,all the other roots of the characteristic equation have real parts that are negative.Moreover,we find the critical values to guarantee the existence of the Bogdanov–Takens bifurcation.In the third step,the normal form is obtained and its dynamical behaviors are studied after the use of the reduction on the center manifold and the theory of the normal form.Furthermore,for the demonstration of our results,we have given a numerical example.展开更多
This paper is concerned with inertial bidirectional associative memory neural networks with mixed delays and impulsive effects.New and practical conditions are given to study the existence,uniqueness,and global expone...This paper is concerned with inertial bidirectional associative memory neural networks with mixed delays and impulsive effects.New and practical conditions are given to study the existence,uniqueness,and global exponential stability of anti-periodic solutions for the suggested system.We use differential inequality techniques to prove our main results.Finally,we give an illustrative example to demonstrate the effectiveness of our new results.展开更多
An Impulsive Multidirectional Associative Memory Neural Network(IMAMNN)with time-varying and leakage delays is proposed.Through the use of a continuation theorem of coincidence degree theory and differential inequalit...An Impulsive Multidirectional Associative Memory Neural Network(IMAMNN)with time-varying and leakage delays is proposed.Through the use of a continuation theorem of coincidence degree theory and differential inequality techniques we establish new conditions for the existence and exponential stability of anti-periodic solutions for the model considered in this work.Moreover,two examples and its numerical simulations are presented to show the validity and the effectiveness of the results.展开更多
In this manuscript, we studied a class of delayed Fuzzy Genetic Regulatory Networks (FGRNs) with Stepanov-like weighted pseudo almost automorphic coefficients. New criteria for the existence, uniqueness and global exp...In this manuscript, we studied a class of delayed Fuzzy Genetic Regulatory Networks (FGRNs) with Stepanov-like weighted pseudo almost automorphic coefficients. New criteria for the existence, uniqueness and global exponential stability of its weighted pseudo almost automorphic solution are established. Our approach is based on Banach fixed point theorem and novel analysis techniques. Moreover, a numerical example is given to illustrate the validity of the obtained results.展开更多
文摘In this paper, we investigate the dynamics and the global exponential stability of a new class of Hopfield neural network with time-varying and distributed delays. In fact, the properties of norms and the contraction principle are adjusted to ensure the existence as well as the uniqueness of the pseudo almost periodic solution, which is also its derivative pseudo almost periodic. This results are without resorting to the theory of exponential dichotomy. Furthermore, by employing the suitable Lyapunov function, some delayindependent sufficient conditions are derived for exponential convergence. The main originality lies in the fact that spaces considered in this paper generalize the notion of periodicity and almost periodicity. Lastly, two examples are given to demonstrate the validity of the proposed theoretical results.
文摘In this paper, we prove the existence and the global exponential stability of the unique weighted pseudo almost-periodic solution of shunting inhibitory cellular neural networks with mixed time-varying delays comprising different discrete and distributed time delays. Some sufficient conditions are given for the existence and the global exponential stability of the weighted pseudo almost-periodic solution by employing fixed point theorem and differential inequality techniques. The results of this paper complement the previously known ones. Finally, an illustrative example is given to demonstrate the effectiveness of our results.
文摘This paper considers the drive-response synchronization in finite-time and fixed-time of inertial neural networks with time-varying and distributed delays(mixed delays). First, by constructing a proper variable substitution, the original inertial neural networks can be rewritten as a first-order differential system. Second, by constructing Lyapunov functions and using differential inequalities,some new and effective criteria are obtained for ensuring the finite-time synchronization. Finally, three numerical examples are also given at the end of this paper to show the effectiveness of the results.
文摘In this paper,a neutral Hopfield neural network with bidirectional connection is considered.In the first step,by choosing the connection weights as parameters bifurcation,the critical point at which a zero root of multiplicity two occurs in the characteristic equation associated with the linearized system.In the second step,we studied the zeros of a third degree exponential polynomial in order to make sure that except the double zero root,all the other roots of the characteristic equation have real parts that are negative.Moreover,we find the critical values to guarantee the existence of the Bogdanov–Takens bifurcation.In the third step,the normal form is obtained and its dynamical behaviors are studied after the use of the reduction on the center manifold and the theory of the normal form.Furthermore,for the demonstration of our results,we have given a numerical example.
文摘This paper is concerned with inertial bidirectional associative memory neural networks with mixed delays and impulsive effects.New and practical conditions are given to study the existence,uniqueness,and global exponential stability of anti-periodic solutions for the suggested system.We use differential inequality techniques to prove our main results.Finally,we give an illustrative example to demonstrate the effectiveness of our new results.
文摘An Impulsive Multidirectional Associative Memory Neural Network(IMAMNN)with time-varying and leakage delays is proposed.Through the use of a continuation theorem of coincidence degree theory and differential inequality techniques we establish new conditions for the existence and exponential stability of anti-periodic solutions for the model considered in this work.Moreover,two examples and its numerical simulations are presented to show the validity and the effectiveness of the results.
文摘In this manuscript, we studied a class of delayed Fuzzy Genetic Regulatory Networks (FGRNs) with Stepanov-like weighted pseudo almost automorphic coefficients. New criteria for the existence, uniqueness and global exponential stability of its weighted pseudo almost automorphic solution are established. Our approach is based on Banach fixed point theorem and novel analysis techniques. Moreover, a numerical example is given to illustrate the validity of the obtained results.
