Functional Dynamical Systems

Murat Adıvar and Youssef N. Raffoul
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Murat Adıvar: Fayetteville State University, Broadwell College of Business and Economics
Youssef N. Raffoul: University of Dayton, Department of Mathematics

Chapter Chapter 3 in Stability, Periodicity and Boundedness in Functional Dynamical Systems on Time Scales, 2020, pp 91-124 from Springer

Abstract: Summary In this chapter we consider functional dynamical systems on time scales that we apply to Volterra integro-dynamic equations on time scales. Volterra integro-dynamic Our general theorems will require the construction of suitable Lyapunov functionals, a task that is difficult but possible. General theorems concerning boundedness and stability of functional dynamical systems on time scales are almost nonexistent and this section is aimed at rectifying the situation. The theorems enable us to qualitatively analyze the theory of boundedness, uniform ultimate boundedness, and stability of solutions of vectors and scalar Volterra integro-dynamic equations. We end the chapter with open problems. Some of the results are new and the rest can be found in Adıvar and Raffoul (Rend Semin Mat Univ Politec Torino 68(4):369–396, 2010), Akın-Bohner and Raffoul (Adv Differ Equ 2006:79689, 18, 2006), and Raffoul (Canad Math Bull 58(1):174–181, 2015; Arch Math 52(1):21–33, 2016).

Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-42117-5_3

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DOI: 10.1007/978-3-030-42117-5_3

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