Info: Zenodo’s user support line is staffed on regular business days between Dec 23 and Jan 5. Response times may be slightly longer than normal.

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

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 Download all
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.