Periodic Solutions Of Neural Networks Research Articles

Pseudo almost periodic synchronization of Clifford-valued fuzzy cellular neural networks with time-varying delays on time scales

At present, the research on discrete-time Clifford-valued neural networks is rarely reported. However, the discrete-time neural networks are an important part of the neural network theory. Because the time scale theory can unify the study of discrete- and continuous-time problems, it is not necessary to separately study continuous- and discrete-time systems. Therefore, to simultaneously study the pseudo almost periodic oscillation and synchronization of continuous- and discrete-time Clifford-valued neural networks, in this paper, we consider a class of Clifford-valued fuzzy cellular neural networks on time scales. Based on the theory of calculus on time scales and the contraction fixed point theorem, we first establish the existence of pseudo almost periodic solutions of neural networks. Then, under the condition that the considered network has pseudo almost periodic solutions, by designing a novel state-feedback controller and using reduction to absurdity, we obtain that the drive-response structure of Clifford-valued fuzzy cellular neural networks on time scales with pseudo almost periodic coefficients can realize the global exponential synchronization. Finally, we give a numerical example to illustrate the feasibility of our results.

The Existence and Global Exponential Stability of Almost Periodic Solutions for Neutral-Type CNNs on Time Scales

In this paper, neutral-type competitive neural networks with mixed time-varying delays and leakage delays on time scales are proposed. Based on the contraction fixed-point theorem, some sufficient conditions that are independent of the backwards graininess function of the time scale are obtained for the existence and global exponential stability of almost periodic solutions of neural networks under consideration. The results obtained are brand new, indicating that the continuous time and discrete-time conditions of the network share the same dynamic behavior. Finally, two examples are given to illustrate the validity of the results obtained.

Global Asymptotic Stability of Periodic Solutions for Discrete Time Delayed BAM Neural Networks by Combining Coincidence Degree Theory with LMI Method

In this paper, we are concerned with the existence and global asymptotic stability of periodic solutions for a class of delayed discrete-time BAM neural networks. Instead of using the method of the priori estimate of periodic solutions in existing papers to study periodic solutions of neural networks, by combining Mawhin’s continuation theorem of coincidence degree theory with linear matrix inequality (LMI) method as well as inequality techniques, some novel LMI-based sufficient conditions to guarantee the existence and global asymptotic stability of periodic solutions for the neural networks are established. Our results which are both dependent on time delay and external inputs of the neural networks are new and complementary to the existing papers.

Global asymptotic stability of periodic solutions for delayed complex-valued Cohen–Grossberg neural networks by combining coincidence degree theory with LMI method

The paper is concerned with the existence and global asymptotic stability of periodic solutions for a class of delayed complex-valued Cohen–Grossberg neural networks. Without using the method of the a priori estimate of periodic solutions, by combining Mawhin’s continuation theorem of coincidence degree theory with LMI method and using inequality techniques, a novel LMI-based sufficient condition on the existence of periodic solutions is established for the complex-valued Cohen–Grossberg neural networks. Then by using inequality techniques, a novel sufficient condition on the global asymptotic stability of periodic solutions for the above complex-valued neural networks is established. Our results and method are new and complementary to the existing papers on the study of periodic solutions of neural networks.

Exponential Stability of Almost Periodic Solutions for Memristor-Based Neural Networks with Distributed Leakage Delays.

In this letter, we deal with a class of memristor-based neural networks with distributed leakage delays. By applying a new Lyapunov function method, we obtain some sufficient conditions that ensure the existence, uniqueness, and global exponential stability of almost periodic solutions of neural networks. We apply the results of this solution to prove the existence and stability of periodic solutions for this delayed neural network with periodic coefficients. We then provide an example to illustrate the effectiveness of the theoretical results. Our results are completely new and complement the previous studies Chen, Zeng, and Jiang ( 2014 ) and Jiang, Zeng, and Chen ( 2015 ).

Stability analysis of neural networks with periodic coefficients and piecewise constant arguments

Global exponential stability of a class of neural networks with periodic coefficients and piecewise constant arguments is investigated in this paper. A new definition of exponential stability and a novel differential inequality with piecewise constant arguments are introduced to obtain sufficient conditions for the globally exponential stability of the periodic solution of neural networks. The stability criteria are independent on the upper bound of the adjacent element difference of the discontinuous switching moments. According to the new definition of exponential stability and the novel differential inequality, not only it is not necessary to establish any relationship between the norms of the states with/without piecewise constant arguments, but also the stability criteria for the neural networks can be obtained just in terms of the original differential equation, rather than the equivalent integral equation which is widely used in the early works. Typical numerical examples are utilized to illustrate the validity and improvement in less conservatism of the theoretical results.

Global convergence of periodic solution of neural networks with discontinuous activation functions

In this paper, without assuming boundedness and monotonicity of the activation functions, we establish some sufficient conditions ensuring the existence and global asymptotic stability of periodic solution of neural networks with discontinuous activation functions by using the Yoshizawa-like theorem and constructing proper Lyapunov function. The obtained results improve and extend previous works.

On periodic solutions of neural networks via differential inclusions

Discontinuous dynamical systems, especially neural networks with discontinuous activation functions, arise in a number of applications and have received considerable research attention in recent years. However, there still remain some fundamental issues to be investigated, for instance, how to define the solutions of such discontinuous systems and what conditions can guarantee the existence and stability of the solutions. In this paper, based on the concept of Filippov solution, the dynamics of a general class of neural networks with discontinuous activation functions is investigated. Sufficient conditions are obtained to ensure the existence and stability of the unique periodic solution for the neural networks by using the differential inclusions theory, the Lyapunov-Krasovskii functional method and linear matrix inequality (LMI) technique. Two numerical examples are given to illustrate the theoretical results.

Stability analysis for periodic solution of neural networks with discontinuous neuron activations

In this paper, we present a general class of neural networks with discontinuous neuron activations and varying coefficients, where the neuron activation function is a discontinuous monotone increasing and bounded function. By using the fixed point theorem in differential inclusion theory and constructing suitable Lyapunov functions, a condition is derived which ensures the existence and global exponential stability of a unique periodic solution for the neural network. Furthermore, under certain conditions global convergence in finite time of the state is investigated. The obtained results show that Forti’s conjecture for neural networks without delays is true. Finally, two numerical examples are given to demonstrate the effectiveness of the results obtained in this paper.

Global exponential stability of periodic solution of neural network with variable coefficients and time-varying delays

By using the continuation theorem of Mawhin’s coincidence degree theory and some inequality techniques, some new sufficient conditions are obtained ensuring existence and global exponential stability of periodic solution of neural networks with variable coefficients and time-varying delays. These results are helpful to design globally exponentially stable and oscillatory neural networks. Finally, the validity and performance of the obtained results are illustrated by two examples.

Analysis of global exponential stability and periodic solutions of neural networks with time-varying delays

In this paper, a general class of recurrent neural networks with time-varying delays is studied. Some novel and sufficient conditions are given to guarantee the global exponential stability of the equilibrium point and the existence of periodic solutions for such delayed neural networks. Comparing with some previous literature, in which the time-varying delays were assumed to be differentiable and their derivatives were simultaneously required to be not greater than 1, the restrictions on the time-varying delays are removed. Therefore, our results obtained here improve and extend some previously related results. Finally, two numerical examples are provided to illustrate our theorems.

Erratum: Exponential stability and periodic solutions of neural networks with continuously distributed delays [Phys. Rev. E67, 011902 (2003)

Erratum: Exponential stability and periodic solutions of neural networks with continuously distributed delays [Phys. Rev. E<b>67</b>, 011902 (2003)

Exponential stability and periodic solutions of neural networks with continuously distributed delays.

In this paper we study a class of neural networks with continuously distributed delays. By means the of Lyapunov functional method, we obtain some sufficient conditions ensuring the existence, uniqueness, and global exponential stability of the equilibrium and periodic solution. We also estimate the exponentially convergent rate. Our results are less restrictive than previously known criteria and can be applied to neural networks with a broad range of activation functions assuming neither differentiability nor strict monotonicity. Moreover, these conclusions are presented in terms of system parameters and can be easily verified. Therefore, our results play an important role in the design of globally exponentially stable neural circuits and periodic oscillatory neural circuits.