Abstract
This chapter is divided into three sections. In Sect. 9.1, we discuss the exponential dichotomies for impulsive dynamic equations on time scales and exponential type of bounds of solutions for three representative impulsive dynamic equations are derived, some new mean-value criteria for exponential dichotomy are obtained and several applications are provided. In Sect. 9.2, we introduce the concept of matrix measure on time scales and conduct an almost periodic analysis of impulsive Lasota-Wazewska model on almost complete-closed translation time scales, and some sufficient conditions for the existence and exponential stability of solutions of the model are established on ACCTS. In Sect. 9.3, a double-almost periodic high-order Hopfield neural networks is proposed and studied, and the existence and ψ-exponential stability of double-almost periodic solutions with slight vibration in time variables are investigated.
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Wang, C., Agarwal, R.P., O’Regan, D., Sakthivel, R. (2020). Analysis of Dynamical System Models on Translation Time Scales. In: Theory of Translation Closedness for Time Scales . Developments in Mathematics, vol 62. Springer, Cham. https://doi.org/10.1007/978-3-030-38644-3_9
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DOI: https://doi.org/10.1007/978-3-030-38644-3_9
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