Almost Periodicity in a Harvesting Lotka-Volterra Recurrent Neural Networks with Time-Varying Delays
Authors: Yongzhi Liao
Abstract:
By using the theory of exponential dichotomy and Banach fixed point theorem, this paper is concerned with the problem of the existence and uniqueness of positive almost periodic solution in a delayed Lotka-Volterra recurrent neural networks with harvesting terms. To a certain extent, our work in this paper corrects some result in recent years. Finally, an example is given to illustrate the feasibility and effectiveness of the main result.
Keywords: positive almost periodic solution, Lotka-Volterra, neural networks, Banach fixed point theorem, harvesting
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1088356
Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1624References:
[1] F. Tomoki, T. Shigeru, A simple neural network exhibiting selective
activation of neuronal ensembles: from winner-take-all to winners-shareall,
Neural Comput. 9 (1997) 77-97.
[2] Y. Moreau, S. Louies, J. Vandewalle, L. Brenig, Embedding recurrent
neural networks into predator-prey models, Neural Networks 12 (1999)
237-245.
[3] Y. Zhang, K. K. Tan, Global convergence of Lotka-Volterra recurrent
neural networks with delays, IEEE Transactions on Circuits and Systems
I: Fundamental Theory and Applications 52 (2005) 2482-2489.
[4] Y. G. Liu, B. B. Liu, S. H. Ling, The almost periodic solution of
Lotka-Volterra recurrent neural networks with delays, Neurocomputing
74 (2011) 1062-1068.
[5] J. Y. Shao, L. J. Wang, C. X. Ou, Almost periodic solutions for shunting
inhibitory cellular neural networks without global Lipschitz activaty
functions, Appl. Math. Model. 33 (2009) 2575-2581.
[6] C. Z. Bai, Existence and stability of almost periodic solutions of Hopfield
neural networks with continuously distributed delays, Nonlinear Anal.:
TMA 71 (2009) 5850-5859.
[7] H. J. Xiang, J. D. Cao, Almost periodic solution of Cohen-Grossberg
neural networks with bounded and unbounded delays, Nonlinear Anal.:
RWA 10 (2009) 2407-2419.
[8] Y. K. Li, X. L. Fan, Existence and globally exponential stability of
almost periodic solution for Cohen-Grossberg BAM neural networks with
variable coefficients, Appl. Math. Model. 33 (2009) 2114-2120.
[9] G. Dai, M. Tang, Coexistence region and global dynamics of a harvested
predator-prey system, SIAM J. Appl. Math. 58 (1998) 193-210.
[10] D. Xiao, L. Jennings, Bifurcations of a ratio-dependent predator-prey
system with constant rate harvesting, SIAM J. Appl. Math. 65 (2005)
737-753.
[11] T. K. Kar, U. K. Pahari, Non-selective harvesting in prey-predator
models with delay, Commun. Nonlinear Sci. Numer. Simulat. 11 (2006)
499-509.
[12] T. K. Kar, A. Ghorai, Dynamic behaviour of a delayed predator-prey
model with harvesting, Appl. Math. Comput. 217 (2011) 9085-9104.
[13] A. M. Fink, Almost Periodic Differential Equation, Spring-Verlag,
Berlin, Heidleberg, New York, 1974.
[14] C. Y. He, Almost Periodic Differential Equations, Higher Education
Press, 1992 (in Chinese).
[15] W. A. Coppel, Dichotomies in Stability Theory, Lecture Notes in
Mathematics, Springer, Berlin, Germany, 1978.
[16] R. P. Agarwal, M. Meehan, D. O’Regan, Fixed Point Theory and
Applications, Cambridge University Press, 2004.