Periodic Solution of Impulsive Lotka-Volterra Recurrent Neural Networks with Delays

Affiliation(s)

School of Mathematics and Statistics, Hainan Normal University, Haikou, Hainan, China.

School of Mathematics and Statistics, Hainan Normal University, Haikou, Hainan, China.

ABSTRACT

In this paper, periodic solution of impulsive Lotka-Volterra recurrent neural networks with delays is studied. Using the continuation theorem of coincidence degree theory and analysis techniques, we establish criteria for the existence of periodic solution of impulsive Lotka-Volterra recurrent neural networks with delays.

Cite this paper

Y. Yan, K. Wang and Z. Gui, "Periodic Solution of Impulsive Lotka-Volterra Recurrent Neural Networks with Delays,"*Open Journal of Applied Sciences*, Vol. 3 No. 1, 2013, pp. 62-64. doi: 10.4236/ojapps.2013.31B1012.

Y. Yan, K. Wang and Z. Gui, "Periodic Solution of Impulsive Lotka-Volterra Recurrent Neural Networks with Delays,"

References

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[1] Z. Jin and M. Zhen, “Periodic Solutions for Delay Differential Equations Model of Plankton Allelopathy,” Computers & Mathematics with Applications, Vol. 44, No. 3-4, 2002, pp. 491-500. doi: 10.1016/S0898-1221(02)00163-3

[2] S. Battaaz and F. Zanolin, “Coexistence States for Periodic Competitive Kolmogorov Systems,” Journal of Mathematical Analysis and Appli-cations, Vol. 219, 1998, pp. 178-199.

[3] S. Arik, “Stability Analysis of Delayed Neural Network,” Fundam. Theory Applications, Vol. 52, 2000, pp. 1089- 1092.

[4] Y. Zhang and K. T. Kok, “Global Convergence of Lotka-Volterra Recurrent Neural Networks with delays,” Circuits and syetemsm, Vol. 52, 2005, pp. 2482-2489.

[5] J. Zhang and Z. J. Gui, “Periodic Solutions of Nonautonomous Cellular Neural Networks with Impulses and Delays,” Real World Applications, Vol. 1, No. 3, 2009, pp. 1891-1903. doi:10.1016/j.nonrwa.2008.02.029

[6] F. Y. Wei and S. H. Wang, “Almost Periodic Solution and Global Stability for Cooperative L-V Diffusion System,” Journal of Mathematical Research and Exposition, Vol. 30, 2010, pp. 1108-1116.

[7] X. Z. Meng and L. S. A. Chen, “Permanence and Global Stability in an Impulsive Lotka-Volterra Species Competitive System with both Discrete Delays and Continuous Delays,” International Journal of Biomathematics, Vol. 1, No. 2, 2008, pp. 179-196. doi: 10.1142/S1793524508000151

[8] R. E. Gaines and J. L. Mawhin, “Coincidence Degree and Nonlinear Deferential Equations,” Berlin: Springer Verlag, 1977.