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Positivity and uniform exponential stability for Volterra integro-dynamical systems on time scales
Affiliation:1. Department of Mathematics, Gazi University, Ankara TR-06500, Turkey;2. Department of Computer Sciences and Applied Mathematics, College Vizioni Për Arsim, Street Ahmet Kaciku Nr. 3, Kati i dyte, Ferizaj 70000, Republic of Kosova;3. Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada;4. Center for General Education, Department of Science and Technology, China Medical University, Taichung 40402, Taiwan, ROC;1. Departamento de Matemática and CMAF-CIO, Faculdade de Ciências, Universidade de Lisboa, Campo Grande, Lisboa 1749-016, Portugal;2. CMAT and Departamento de Matemática e Aplicações, Escola de Ciências, Universidade do Minho, Campus de Gualtar, Braga 4710-057, Portugal
Abstract:The main objective of this study is two-fold: First, we provide necessary and sufficient conditions for the positivity of Volterra integro-dynamical systems on time scales by means of Metzler matrices. Secondly, we show that positivity of the system implies uniform exponential stability of the trivial solution under sufficient conditions.
Keywords:Time scale  Volterra integro-dynamical system  Metzler matrix  Positive system  Uniform exponential stability
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