Acta mathematica scientia,Series A ›› 2024, Vol. 44 ›› Issue (6): 1563-1576.
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Received:
2024-01-23
Revised:
2024-05-06
Online:
2024-12-26
Published:
2024-11-22
Supported by:
CLC Number:
Zhang Yiran, Li Dingshi. Invariant Measure of Impulsive Fractional Lattice System[J].Acta mathematica scientia,Series A, 2024, 44(6): 1563-1576.
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[1] | Chow S N. Lattice dynamical systems. Lect Notes Math, 2003, 1822: 1-102 |
[2] | Chow S N, Paret J M. Pattern formation and spatial chaos in lattice dynamical systems. IEEE Trans Circuits Syst, 1995, 42: 752-756 |
[3] | Keener J P. Propagation and its failure in coupled systems of discret excitable cells. SIAM J Appl Math, 1987, 47: 556-572 |
[4] | Caraballo T, Morillas F, Valero J, Differ J. Attractors of stochastic lattice dynamical systems with a multipliative noise and non-Lipschitz nonlinearities. J Differ Equ, 2012, 253(2): 667-693 |
[5] | Jia X, Zhao C, Yang X. Global attractor and Kolmogorov entropy of three component reversible gray-scott model on infinite lattices. Appl Math Comput, 2012, 218: 9781-9789 |
[6] | Zhou S, Shi W. Attractors and dimension of dissipative lattice systems. J Differ Equ, 2006, 224: 172-204 |
[7] | Bates P W, Lisei H, Lu K. Attractors for stochastic lattice dynamical systems. Stochastics and Dynamics, 2006, 6: 1-21 |
[8] | Bates P W, Lu K, Wang B. Attractors of non-autonomous stochastic lattice systems in weighted spaces. Physica D: Nonlinear Phenomena, 2014, 289: 32-50 |
[9] | Chen Z, Li X, Wang B. Invariant measures of stochastic delay lattice systems. Discrete & Continuous Dynamical Systems-Series B, 2021, 26: 3235 |
[10] | Liu X, Ballinger G. Uniform asymptotic stability of impulsive delay differential equations. Comput Math Appl, 2001, 903-915 |
[11] | Bainov D D, Simenov P S. Systems with Impulse Effect:Stability Theory and Applications. Chichester New York: Ellis Horwood Halsted Press, 1989 |
[12] | Ciaurri O, Gillespie T A, Roncal L, et al. Harmonic analysis associated with a discrete Laplacian. J Anal Math, 2017, 132: 109-131 |
[13] | Ciaurri O, Roncal L, Stinga P R, et al. Global attractors for impulsive dynamical systems--a precompact approach. Adv Math, 2018, 330: 688-738 |
[14] | Łukaszewicz, Real G, Robinson J. Invariant measures for dissipative dynamical systems and generalised Banach limits. J Dyn Differ Equ, 2011, 225-250 |
[15] | Zhao C, Xue G, Łukaszewicz. Pullback attractors and invariant measures for discrete Klein-Gordon-Schrödinger equations. Discrete Contin Dyn Syst, 2018, 23B: 4021-4044 |
[16] | Zhao C, Caraballo. Statistical solutions and piecewise Liouville theorem for the impulsive reaction-diffusion equations on infinite lattices. Appl Math Comput, 2021, 404: 126103 |
[17] | Ciaurri O, Roncal L, Stinga P R, et al. Nonlocal discrete diffusion equations and the fractional discrete Laplacian, regularity and applications. Adv Math, 2018, 330: 688-738 |
[18] | Bainov D, Simeonov P S. Impulsive differential equations: Periodic solutions and applications. Longman Scientific, 1993: 173-178 |
[19] | Chen Y, Wang X. Asymptotic behavior of non-autonomous fractional stochastic lattice systems tiplicative noise. Discrete & Continuous Dynamical Systems-Series B, 2022, 27(9): 5205-5224 |
[20] | Łukaszewicz G, Robinson J C. Invariant measures for non-autonomous dissipative dynamical systems. Discrete Contin Dyn Syst, 2014, 34(10): 4211-4222 |
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