**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30172

##### Pseudo-almost Periodic Solutions of a Class Delayed Chaotic Neural Networks

**Authors:**
Farouk Cherif

**Abstract:**

This paper is concerned with the existence and unique¬ness of pseudo-almost periodic solutions to the chaotic delayed neural networks (t)= —Dx(t) ± A f (x (t)) B f (x (t — r)) C f (x(p))dp J (t) . t-o Under some suitable assumptions on A, B, C, D, J and f, the existence and uniqueness of a pseudo-almost periodic solution to equation above is obtained. The results of this paper are new and they complement previously known results.

**Keywords:**
Chaotic neural network,
Hamiltonian systems,
Pseudo almost periodic.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1055713

**References:**

[1] G. Prouse, Almost-Periodic Functions and Functional Analysis, von Nostrand Reinhold Co., New York, 1971.

[2] M. Adachi, and K. Aihara, Associative dynamics in a chaotic neural network. Neural Networks, (1997). 10, 83-98.

[3] B. Amir, L. Maniar, Composition of Pseudo Almost Periodic Functions and Cauchy Problems with Operators of non Dense Domain, Ann. Math. Blaise Pascal, 6 (1999), 1-11.

[4] A. S. Besicovitch, Almost periodic functions, Cambridge University Press,1932.

[5] S. Blythe, X. Mao and X. Liao, Stability of stochastic delay neural networks, J Franklin Inst 338 (2001), pp. 481-495.

[6] B. Cannas, S. Cincotti, M. Marchesi and F. Pilo, Learning of Chua's circuit attractors by locally recurrent neural networks, Chaos, Solitons Fractals 12 (2001), pp. 2109-2115.

[7] J. Cao, New results concerning exponential stability and periodic solu¬tions of delayed cellular neural networks, Phys. Lett. A 307 (2003) 136 147.

[8] J. Cao, A. Chen, X. Huang, Almost periodic attraction of delayed neural networks with variable coefficients, Phys. Lett. A 340 (2005) 104 120.

[9] Q. Dong, K. Matsui, X. Haung, Existence and stability of periodic solutions for Hopfield neural network equations with periodic input, Nonlinear Anal. 49 (2002) 471-479.

[10] A. M. Fink, Almost periodic differential equations, Springer, Berlin, 1974.

[11] Z. Gui, W. Ge, X. Yang, Periodic oscillation for a Hopfield neural networks with neutral delays, Phys. Lett. A 364 (2007) 267-273.

[12] S. Guo, L. Huang, Periodic solutions in an inhibitory two-neuron network, J. Comput. Appl. Math. 161 (2003) 217-229.

[13] J. Hopfield, Neurons with graded response have collective computational properties like those of two-state neurons, Proc Nat Acad Sci USA 81 (1984), pp. 3088-3092.

[14] H. Huang, J. Cao, J. Wang, Global exponential stability and periodic solutions of recurrent cellular neural networks with delays, Phys. Lett. A 298 (2002)393 404.

[15] B. Liu and L. Huang, Existence and stability of almost periodic solutions for shunting inhibitory cellular neural networks with time-varying delays, Chaos, Solitons Fractals 31 (2007), pp. 211-217.

[16] B. Liu, L. Huang, Existence and global exponential stability of almost periodic solutions for Hopfield neural networks with delays, Neurocom¬puting 68 (2005) 196-207.

[17] Z. Liu, A. Chen, J. Cao, L. Huang, Existence and global exponential stability of almost periodic solutions of BAM neural networks with continuously distributed delays, Phys. Lett. A 319 (2003) 305 316.

[18] B. Liu, Almost periodic solutions for Hopfield neural networks with continuously distributed delays, Math. Comput. Simulation 73 (2007) 327-335.

[19] R. Marichal, J.D. Pifieiro, E. Gonzalez and J. Torres, Analysis of Saddle-Node Bifurcation in a small Discrete Hopfield Neural Network, IAENG International Journal of Computer Science, 37:2, IJCS_37_2_07.

[20] K. Otawara, L. Fan, A. Tsutsumi, T. Yano, K. Kuramoto and K. Yoshida, An artificial neural network as a model for chaotic behavior of a three-phase fluidized bed, Chaos, Solitons Fractals 13 (2002), pp. 353-362.

[21] C. Quek, K.B. Tan and V.K. Sagar, Pseudo-outer product based fuzzy neural networks finger print verification system, Neural Networks 14 (2001), pp. 305-323.

[22] M. Ramesh and S. Narayanan, Chaos control of Bonhoeffer-van der Pol oscillator using neural networks, Chaos, Solitons Fractals 12 (2001), pp. 2395-2405.

[23] V. Singh, Robust stability of cellular neural networks with delay: linear matrix inequality approach, IEEE Proc Control Theory Appl 151 (2004), pp. 125-129.

[24] B. Xiao, Existence and uniqueness of almost periodic solutions for a class of Hopfield neural networks with neutral delays, Appl. Math. Lett.Volume 22, Issue 4, April 2009, Pages 528-533.

[25] C. Zhang, Pseudo almost periodic functions and their applications, Ph.D. thesis, University of Western Ontario, (1992).

[26] C. Zhang, Almost Periodic Type Functions and Ergodicity. Kluwer Academic Publishers and Science Press, Beijing, 2003.