Exponential Stability Of Anti-periodic Solutions Research Articles

Stability Analysis of Anti-Periodic Solutions for Cohen–Grossberg Neural Networks with Inertial Term and Time Delays

This work is dedicated to exploring the globally exponential stability of anti-periodic solutions in inertial CGNNs that incorporate time delays. This is based on a strategic variable substitution to transform the complex system into a first-order differential equation. By leveraging the Lyapunov functional and demonstrating uniformly converging properties, we establish sufficient conditions that guarantee the existence and global exponential stability of anti-periodic solutions for the system. Finally, examples are presented to illustrate the effectiveness of the obtained theoretical results. This work contributes significantly to enhancing our understanding of the stability dynamics in neural networks with time delays and provides valuable insights for applications across various fields.

Anti-periodic problem for semilinear differential inclusions involving Hille-Yosida operators

In this paper we are interested in the anti-periodic problem governed by a class of semilinear differential inclusions with linear parts generating integrated semigroups. By adopting the Lyapunov-Perron method and the fixed point argument for multivalued maps, we prove the existence of anti-periodic solutions. Furthermore, we study the long-time behavior of mild solutions in connection with anti-periodic solutions. Consequently, as the nonlinearity is of single-valued, we obtain the exponential stability of anti-periodic solutions. An application of theoretical results to a class of partial differential equations will be given.

Impulsive multidirectional associative memory neural networks: New results

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.

Anti-periodic behavior for quaternion-valued delayed cellular neural networks

In this manuscript, quaternion-valued delayed cellular neural networks are studied. Applying the continuation theorem of coincidence degree theory, inequality techniques and a Lyapunov function approach, a new sufficient condition that guarantees the existence and exponential stability of anti-periodic solutions for quaternion-valued delayed cellular neural networks is presented. The obtained results supplement some earlier publications that deal with the anti-periodic solutions of quaternion-valued neural networks with distributed delay or impulse or state-dependent delay or inertial term. Computer simulations are displayed to check the derived analytical results.

Anti-periodicity on high-order inertial Hopfield neural networks involving mixed delays

This paper deals with a class of high-order inertial Hopfield neural networks involving mixed delays. Utilizing differential inequality techniques and the Lyapunov function method, we obtain a sufficient assertion to ensure the existence and global exponential stability of anti-periodic solutions of the proposed networks. Moreover, an example with a numerical simulation is furnished to illustrate the effectiveness and feasibility of the theoretical results.

Existence and exponential stability of anti-periodic solution for fuzzy BAM neural networks with inertial terms and time-varying delays

In this paper, the existence and exponential stability of anti-periodic solutions for fuzzy BAM neural networks with inertial terms and time-varying delays is investigated. Firstly, some sufficient conditions ensuring the existence of anti-periodic solutions of the system are obtained by employing a new continuation theorem of coincidence degree theory. Secondly, by constructing an appropriate Lyapunov function, some sufficient conditions are derived to guarantee the global exponential stability of anti-periodic solutions of the system. Our results of this paper are completely new. Finally, two numerical examples are given to show the effectiveness of the obtained results.

Antiperiodic solutions to delayed inertial quaternion‐valued neural networks

This manuscript mainly deals with quaternion‐valued neural networks (QVNNs) with delays and inertial term. Using Wirtinger inequality and coincidence degree theory, a new sufficient criterion to ensure the existence of antiperiodic solution of involved quaternion‐valued neural networks is derived. With the aid of Lyapunov function, we discuss the exponential stability of antiperiodic solutions to quaternion‐valued neural networks. Numerical simulations are presented to illustrate the established theoretical findings.

Global exponential stability of anti-periodic solutions for discontinuous Cohen–Grossberg neural networks with time-varying delays

ABSTRACT This paper presents a class of Cohen–Grossberg neural networks (CGNNs) with discontinuous activations and time-varying delays. Firstly, under the framework of Filippov solution, we derive some general sufficient conditions to guarantee the global existence of the solutions to the proposed CGNNs with discontinuous activations and time-varying delays. Then, by constructing the new Lyapunov–Krasovskii functional, some new sufficient criteria are given to ascertain the globally exponential stability of the anti-periodic solution for the considered CGNNs with discontinuous activations and time-varying delays. To the authors’ knowledge, the results established in the paper are the only available results on the anti-periodic for the discontinuous CGNNs; some previously known results are extended and complemented. Finally, simulation results of two typical numerical examples are also delineated to demonstrate the effectiveness of our theoretical results.

Anti-periodic Oscillations of Fuzzy Delayed Cellular Neural Networks with Impulse on Time Scales

In this manuscript, fuzzy delayed cellular neural networks with impulse are studied. Applying time scale calculus knowledge, mathematical inequalities and constructing Lyapunov function, we establish a sufficient criterion that guarantees the existence and exponential stability of anti-periodic solutions for fuzzy delayed cellular neural networks with impulse. In addition, an example with its numerical simulations is given to illustrate our theoretical predictions.

New results on impulsive type inertial bidirectional associative memory neural networks

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.

Existence and global exponential stability of anti-periodic solutions for quaternion-valued cellular neural networks with time-varying delays

In this paper, we are concerned with a class of quaternion-valued cellular neural networks with time-varying transmission delays and leakage delays. By applying a continuation theorem of coincidence degree theory and the Wirtinger inequality as well as constructing a suitable Lyapunov functional, sufficient conditions are derived to ensure the existence and global exponential stability of anti-periodic solutions via direct approaches. Our results are completely new. Finally, numerical examples are also provided to show the effectiveness of our results.

Existence and global exponential stability of anti-periodic solutions for generalised inertial competitive neural networks with time-varying delays

ABSTRACTIn this paper, a class of generalised inertial competitive neural networks with time-varying delays is proposed. The existence and global exponential stability of anti-periodic solutions for this class of neural networks are investigated. By using a continuation theorem of coincidence degree theory, the Wirtinger inequality and constructing an appropriate Lyapunov function, some sufficient conditions are derived to guarantee the existence, uniqueness, and global exponential stability of anti-periodic solutions for the considered networks. Our results are completely new.

Anti-periodic oscillations in fuzzy cellular neural networks with time-varying delays

ABSTRACTThis article mainly studies delayed fuzzy cellular neural networks. A sufficient criterion to guarantee the existence and exponential stability of anti-periodic solutions for this system is given. An example is given to support the obtained theoretical analysis. The obtained results play an important role in designing the neural networks and complement the earlier publications.

Existence and Exponential Stability of Anti-Periodic Solutions for Inertial Quaternion-Valued High-Order Hopfield Neural Networks With State-Dependent Delays

This paper deals with a class of inertial quaternion-valued high-order Hopfield neural networks with state-dependent delays. Without decomposing the considered neural networks into real-valued systems, based on a continuation theorem of coincidence degree theory and the Wirtinger inequality, the existence of anti-periodic solutions of the networks is established. By constructing a suitable Lyapunov function, the global exponential stability of anti-periodic solutions of the networks is obtained. Finally, a numerical example is given to show the feasibility of our results.

Anti-periodic solutions for fractional-order bidirectional associative memory neural networks with delays

This paper concerns fractional-order bidirectional associative memory neural networks with distributed delays. Based on inequality technique and Lyapunov functional method, some novel sufficient conditions are obtained for the existence and exponential stability of anti-periodic solutions are established. An example is given to show the feasibility main results.

Existence and global exponential stability of anti-periodic solution for Clifford-valued inertial Cohen–Grossberg neural networks with delays

In this paper, we are concerned with a class of Clifford-valued inertial Cohen-Grossberg neural networks with time-varying delays. Based on the coincidence degree theory and the Wirtinger inequality, we first obtain sufficient conditions ensuring the existence of anti-periodic solutions for this class of networks. Then, by constructing a suitable Lyapunov functional, we establish the global exponential stability of the anti-periodic solutions. Our results are completely new even if the considered neural networks degenerate into real-valued, complex-valued or quaternion-valued. Finally, we present a numerical example to show the effectiveness of our results

Exponential Stability of Antiperiodic Solution for BAM Neural Networks with Time-Varying Delays

In this paper, a kind of BAM neural networks with leakage delays in the negative feedback terms and time-varying delays in activation functions was considered. By constructing a suitable Lyapunov function and using inequality techniques, some sufficient conditions to ensure the existence and exponential stability of antiperiodic solutions of these neural networks were derived. These conditions extend some results recently appearing in recent papers. Lastly, an example is given to show the feasibility of these conditions.

Antiperiodic Solutions for Quaternion-Valued Shunting Inhibitory Cellular Neural Networks with Distributed Delays and Impulses

This paper is concerned with quaternion-valued shunting inhibitory cellular neural networks (QVSICNNs) with distributed delays and impulses. By using a new continuation theorem of the coincidence degree theory, the existence of antiperiodic solutions for QVSICNNs is obtained. By constructing a suitable Lyapunov function, some sufficient conditions are derived to guarantee the global exponential stability of antiperiodic solutions for QVSICNNs. Finally, an example is given to show the feasibility of obtained results.

Anti-Periodic Dynamics of Quaternion-Valued Fuzzy Cellular Neural Networks with Time-Varying Delays on Time Scales

A class of quaternion-valued fuzzy cellular neural networks with time-varying delays on time scales is proposed. Based on inequality analysis techniques on time scales, a fixed point theorem and the theory of calculus on time scales, the existence, and global exponential stability of anti-periodic solutions for this class of neural networks are established. The obtained results are completely new and supplement to the known results. Finally, a numerical example is given to illustrate the feasibility of our results.

Anti-periodic Solutions for Quaternion-Valued High-Order Hopfield Neural Networks with Time-Varying Delays

In this paper, quaternion-valued high-order Hopfield neural networks (QVHHNNs) with time-varying delays are considered. Theoretically, a QVHHNN can be separated into four real-valued systems, forming an equivalent real-valued system. By using a novel continuation theorem of coincidence degree theory and constructing an appropriate Lyapunov function, some sufficient conditions are derived to guarantee the existence and global exponential stability of anti-periodic solutions for QVHHNN, which are new and complement previously known results.