The existence and stability of the anti-periodic solution for delayed Cohen–Grossberg neural networks with impulsive effects

Abdurahman, Abdujelil; Jiang, Haijun

doi:10.1016/j.neucom.2013.09.071

Cited by 31 publications

(11 citation statements)

References 20 publications

(31 reference statements)

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“…Based on a novel method that is different from those used in [10,[25][26][27][28][29][30][31][32][33][34], we established the existence and global exponential stability of anti-periodic solutions of the QVFCNNs. To the best of our knowledge, this is the first paper to study the existence of anti-periodic solutions for QVFCNNs with time-varying delays on time scales.…”

Section: Resultsmentioning

confidence: 99%

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

Shen

2018

Discrete Dynamics in Nature and Society

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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.

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Section: Resultsmentioning

confidence: 99%

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

Shen

2018

Discrete Dynamics in Nature and Society

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“…Remark In Theorem , we do not require the activation functions to be bounded. But, in recent works,() the activation functions are assumed to be bounded. If we assume that the activation functions are bounded, then we have the following verifiable results.…”

Section: The Existence Of Anti‐periodic Solutionsmentioning

confidence: 99%

“…So, in order to analyze the dynamical behaviors to neural networks, incorporating time delays and impulsive effects into them is a nature and necessary step. Numerous results on impulsive effects have been gained for delayed neural networks, see previous studies() and the references therein.…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, it is well known that anti‐periodicity is an important dynamical behavior for neural networks because signal transmission process of neural networks can often be described as an anti‐periodic process. () At present, there have been published many papers on anti‐periodic oscillations of neural networks. However, to the best of our knowledge, the anti‐periodic oscillation of QVNNs with time‐varying delays and impulsive effects has not been reported yet.…”

Section: Introductionmentioning

confidence: 99%

“…Our results are new even when system is degenerated into a real‐valued system, and our method is different from those used in other studies. ()…”

Section: Introductionmentioning

confidence: 99%

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Existence and global exponential stability of anti‐periodic solutions for delayed quaternion‐valued cellular neural networks with impulsive effects

Qin

2018

Math Methods in App Sciences

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In this paper, we consider a class of delayed quaternion-valued cellular neural networks (DQVCNNs) with impulsive effects. By using a novel continuation theorem of coincidence degree theory, the existence of anti-periodic solutions for DQVCNNs is obtained with or without assuming that the activation functions are bounded. Furthermore, by constructing a suitable Lyapunov function, some sufficient conditions are derived to guarantee the global exponential stability of anti-periodic solutions for DQVCNNs. Our results are new and complementary to the known results even when DQVCNNs degenerate into real-valued or complex-valued neural networks. Finally, an example is given to illustrate the effectiveness of the obtained results. KEYWORDSanti-periodic solution, neural networks, quaternion, stabilitywhere q 0 , q 1 , q 2 , q 3 are real numbers and the elements i, j, and k obey the Hamilton's multiplication rules:In the past two decades, the theory of quaternion has been found a lot of applications in many fields such as such as attitude control, quantum mechanics, robotics, computer graphics, and so on. 26-30 Quaternion-valued neural networks (QVNNs), Math Meth Appl Sci. 2019;42:5-23.wileyonlinelibrary.com/journal/mma

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Antiperiodic solutions to delayed inertial quaternion‐valued neural networks

Liao

et al. 2020

Math Methods in App Sciences

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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.

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The existence and stability of the anti-periodic solution for delayed Cohen–Grossberg neural networks with impulsive effects

Cited by 31 publications

References 20 publications

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

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

Existence and global exponential stability of anti‐periodic solutions for delayed quaternion‐valued cellular neural networks with impulsive effects

Antiperiodic solutions to delayed inertial quaternion‐valued neural networks

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