JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (10): 97-108.doi: 10.6040/j.issn.1671-9352.0.2018.600

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Almost automorphic solutions for shunting inhibitory cellular neural networks with leakage delays on time scales

DAI Li-hua, HUI Yuan-xian*   

  1. School of Mathematics and Statistics, Puer University, Puer 665000, Yunnan, China
  • Published:2019-10-12

Abstract: Shunting inhibitory cellular neural networks(SICNNs)with time-varying delays in the leakage term and continuously distributed delays on time scale T is proposed. Based on the exponential dichotomy of linear dynamic equation on time scales, fixed point theorems on time scales, we obtain some new sufficient conditions for the existence a global exponential stability of almost automorphic solution for the class of neural networks. Moreover, we give convictive numerical examples to show the feasibility of our results. This paper contains the several classes of functional differential equations, including the existence of solutions and the stability of this solution on time scales. Also, some new results are obtained.

Key words: almost automorphic solution, time scale, shunting inhibitory neural network, global exponential stability

CLC Number: 

  • O193
[1] MCCULLOCCH W S, PITTS W A. Logical calculus of the ideas immanent in nervous activity[J]. Bulletin of Mathematical Biophysics, 1943, 5:115-133.
[2] HOPFIELD J J. Neural network and physical system with emergent collective computational abilities[J]. Proceedings of the National Academy of Sciences, 1982, 79(8):2554-2558.
[3] HOPFIELD J J. Neurons with graded response have collective computational properties like those of two-stage neurons[J]. Proceedings of the National Academy of Sciences, 1984, 81(10):3088-3092.
[4] BOUZERDOUM A, PINTER P B. Analysis and analog implementaion of directionally sensitive shunting inhibitory neural networks[J]. Proceedings of the SPIE, 1991, 1473(1):29-38.
[5] LI Yongkun, WANG Lei, FEI Yu. Periodic solution for shunting inhibitory cellular neural networks of neutral with time-varying delays in the leakage term on time scales[J]. Applied Mathematics, 2014, 2014(1):1-16.
[6] LI Yongkun, WANG Chao. Almost periodic solutions of shuntin inhibitory cellular neural networks on time scales[J]. Commun Nonlinear Sci Numer Simulat, 2012, 17(8):3258-3266.
[7] NGUÉRÉKATA G M. Existence and uniqueness of almost automorphic mild solutions to some semilinear abstract differential equation[J]. Semigroup Forum, 2004, 69(1):80-89.
[8] GOLDSTEIN J A, NGUÉRÉKATA G M. Almost automorphic solutions of semilinear evolution equations[J]. Proceedings of the American Mathematical Society, 2005, 133(8):2401-2408.
[9] EZZINBI K, FATAJOU S, NGUÉRÉKATA G M. A Cn-almost automorphic solutions for partial neutral functional differential equations[J]. Applicable Analysis, 2007, 86(9):1127-1146.
[10] HILGER S. Ein Maβkettenkalkül mit Anwendung auf Zentrumsmannigfaltigkeiten[D]. Würzburg: Universität Würzburg, 1988.
[11] BALASUBRAMANIAM P, NAGAMANI G, RAKKIYAPPAN R. Passivity analysis for neural networks of neutral type with Markovian jumping parameters and time delay in the leakage term[J]. Communications in Nonlinear Science and Numerical Simulation, 2011, 16(11):4422-4437.
[12] LI Xiaodi, CAO Jinde. Delay-dependent stability of neural networks of neutral type with time delay in the leakege term[J]. Nonlinearity, 2010, 23(7):1709-1726.
[13] BOHNER M, PETERSON A. Dynamic equations on time scales: an introduction with applications[M]. Boston: Birkhäuser, 2001.
[14] LI Yongkun, WANG Chao. Uniformly almost periodic functions and almost periodic solutions to dynamic equations on time scales[J]. Abstract and Applied Analysis, 2011(Article ID 341520):1-22. DOI:10.1155/2011/341520.
[15] LI Yongkun, LI Yang.Almost automorphic solutin for neutral type high-order Hopfield neural networks with delays in leakage terms terms on time scales[J]. Applied Mathematics and Computation, 2014(1), 242:679-693.
[16] LIZAMA C, MESQUITA J G. Almost automorphic solutions of dynamic equations on time scales[J]. Journal of Functional Analysis, 2013, 265(10):2267-2311.
[17] LI Yongkun,WANG Huimei, MENG Xianfang. Almost automorphic synchronization of quaternion-valued high-order Hopfield neural networks with time-varying and distributed delays[J]. IMA Journal of Mathematical Control and Information, 2018, 2018(00):1-31.
[18] XU Changjin, LI Peiluan. On anti-periodic solutions for neutral shunting inhibitory cellular neural networks with time-varying delays and D operator[J]. Neurocomputing, 2018, 275(1):377-382.
[19] XU Changjin, LI Peiluan. Periodic dynamics for memristor-based bidirectional associative memory neural networks with leakage delays and time-varying delays[J]. Control Automation and Systems, 2018, 16(2):535-549.
[20] LONG Zhiwen. New results on anti-periodic solutions for SICNNs with oscillating coefficients in leakage terms[J]. Neuro-computing, 2016, 171(1):503-509.
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