World Academy of Science, Engineering and Technology
Published January 24, 2010 | Version 14295
Journal article Open

Existence and Stability of Anti-periodic Solutions for an Impulsive Cohen-Grossberg SICNNs on Time Scales

Authors/Creators

Description

By using the method of coincidence degree and constructing suitable Lyapunov functional, some sufficient conditions are established for the existence and global exponential stability of antiperiodic solutions for a kind of impulsive Cohen-Grossberg shunting inhibitory cellular neural networks (CGSICNNs) on time scales. An example is given to illustrate our results.

Files

14295.pdf

Files (223.1 kB)

Name Size
md5:49065ca0dc6ef569cfe8f96ef62477c9
223.1 kB Preview Download

Additional details

References

  • A. Bouzerdoum, R.B. Pinter, Shunting inhibitory cellular neural networks: Derivation and stability analysis, IEEE Trans. Circuits Syst. 1-Fund. Theory Appl. 40 (1993) 215-221.
  • X.S. Yang, Existence and global exponential stability of periodic solution for Cohen-Grossberg shunting inhibitory cellular neural networks with delays and impulses, Neurocomputing 72 (2009) 2219-2226.
  • Y.H. Xia, J.D. Cao, Z.K. Huang, Existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with impulses, Chaos, Solitons & Fractals 34 (2007) 1599-1607.
  • L. Chen, H.Y. Zhao, Global stability of almost periodic solution of shunting inhibitory cellular neural networks with variable coefficients, Chaos, Solitons & Fractals 35 (2008) 351-357.
  • Y.Q. Li, H. Meng, Q.Y. Zhou, Exponential convergence behavior of shunting inhibitory cellular neural networks with time-varying coefficients, J. Comput. Appl. Math. 216 (2008) 164-169.
  • J.Y. Shao, An anti-periodic solution for a class of recurrent neural networks, J. Comput. Appl. Math. 228 (2009) 231-237.
  • J.Y. Shao, Anti-periodic solutions for shunting inhibitory cellular neural networks with time-varying delays, Phys. Lett. A 372 (2008) 5011-5016.
  • Y.K. Li, L. Yang, Anti-periodic solutions for Cohen-Grossberg neural networks with bounded and unbounded delays, Commun. Nonlinear Sci. Numer. Simulat. 14 (2009) 3134-3140.
  • G.Q. Peng, L.H. Huang, Anti-periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays, Nonlinear Anal.: Real World Appl. 10 (2009) 2434-2440. [10] Q.Y. Fan, W.T. Wang, X.J. Yi, Anti-periodic solutions for a class of nth-order differential equations with delay, J. Comput. Appl. Math. 230 (2009) 762-769. [11] E.R. Kaufmann, Y.N. Raffoul, Periodic solutions for a neutral nonlinear dynamical equation on a time scale, J. Math. Anal. Appl. 319 (2006) 315-325. [12] M. Bohner, A. Peterson, Dynamic equations on time scales: An introduction with applications, Boston, Birkhauser. 2001. [13] M. Bohner, M. Fan, J. Zhang, Existence of periodic solutions in predatorprey and competition dynamic systems, Nonlinear Analysis: Real World Appl. 7 (2006) 1193-1204. [14] G. Guseinov, Integration on time scales, J. Math. Anal. Appl. 285(2003) 107-127. [15] D. O-Regan, Y.J. Cho, Y.Q. Chen, Topological degree theory and application, Taylor & Francis Group, Boca Raton, London, New York, 2006. [16] Y.K. Li, X.R. Chen, L. Zhao, Stability and existence of periodic solutions to delayed Cohen-Grossberg BAM neural networks with impulses on time scales, Neurocomputing 72 (2009) 1621-1630.