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Global Exponential Stability of Almost Periodic Solution for Neutral-Type Cohen-Grossberg Shunting Inhibitory Cellular Neural Networks with Distributed Delays and Impulses.

Xu L, Jiang Q, Gu G - Comput Intell Neurosci (2016)

Bottom Line: Firstly, by using the theory of impulsive differential equations and the contracting mapping principle, the existence and uniqueness of the almost periodic solution for the above system are obtained.The work in this paper improves and extends some results in recent years.As an application, an example and numerical simulations are presented to demonstrate the feasibility and effectiveness of the main results.

View Article: PubMed Central - PubMed

Affiliation: School of Mathematics and Computer Science, Panzhihua University, Panzhihua, Sichuan 617000, China.

ABSTRACT
A kind of neutral-type Cohen-Grossberg shunting inhibitory cellular neural networks with distributed delays and impulses is considered. Firstly, by using the theory of impulsive differential equations and the contracting mapping principle, the existence and uniqueness of the almost periodic solution for the above system are obtained. Secondly, by constructing a suitable Lyapunov functional, the global exponential stability of the unique almost periodic solution is also investigated. The work in this paper improves and extends some results in recent years. As an application, an example and numerical simulations are presented to demonstrate the feasibility and effectiveness of the main results.

No MeSH data available.


Exponential stability of state variables u21 of system (52).
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fig6: Exponential stability of state variables u21 of system (52).

Mentions: Also, by utilizing the MATLAB dde23, Figures 3–7 depict the time responses of state variables (u11, u12, u21, u22)T in system (54) with step 0.01, respectively. It confirms that the proposed condition in Theorem 11 leads to globally exponentially stable almost periodic solution for system (54).


Global Exponential Stability of Almost Periodic Solution for Neutral-Type Cohen-Grossberg Shunting Inhibitory Cellular Neural Networks with Distributed Delays and Impulses.

Xu L, Jiang Q, Gu G - Comput Intell Neurosci (2016)

Exponential stability of state variables u21 of system (52).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4829795&req=5

fig6: Exponential stability of state variables u21 of system (52).
Mentions: Also, by utilizing the MATLAB dde23, Figures 3–7 depict the time responses of state variables (u11, u12, u21, u22)T in system (54) with step 0.01, respectively. It confirms that the proposed condition in Theorem 11 leads to globally exponentially stable almost periodic solution for system (54).

Bottom Line: Firstly, by using the theory of impulsive differential equations and the contracting mapping principle, the existence and uniqueness of the almost periodic solution for the above system are obtained.The work in this paper improves and extends some results in recent years.As an application, an example and numerical simulations are presented to demonstrate the feasibility and effectiveness of the main results.

View Article: PubMed Central - PubMed

Affiliation: School of Mathematics and Computer Science, Panzhihua University, Panzhihua, Sichuan 617000, China.

ABSTRACT
A kind of neutral-type Cohen-Grossberg shunting inhibitory cellular neural networks with distributed delays and impulses is considered. Firstly, by using the theory of impulsive differential equations and the contracting mapping principle, the existence and uniqueness of the almost periodic solution for the above system are obtained. Secondly, by constructing a suitable Lyapunov functional, the global exponential stability of the unique almost periodic solution is also investigated. The work in this paper improves and extends some results in recent years. As an application, an example and numerical simulations are presented to demonstrate the feasibility and effectiveness of the main results.

No MeSH data available.