Nonlinear differential equations and dynamical systems
Nonlinear differential equations and dynamical systems
Stability criteria for impulsive systems on time scales
Journal of Computational and Applied Mathematics
Stability and periodicity in dynamic delay equations
Computers & Mathematics with Applications
Qualitative behavior of SIS epidemic model on time scales
ASM'10 Proceedings of the 4th international conference on Applied mathematics, simulation, modelling
The effect of time scales on SIS epidemic model
WSEAS Transactions on Mathematics
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In this paper we examine the stability and instability of the equilibrium solution x = 0 to the first-order system of dynamic equations x^@D=f(t,x),t=t"0,x@?D@?R^n,where t is from a so-called time scale T with t"0 @? Tand D is a compact set. Our methods involve the existence of a positive definite Liapunov function V, such that its delta-derivative V^@D satisfies certain integral, definite or semidefinite sign properties. Finally, we use Liapunov functions to develop an invariance principle regarding solutions to the above dynamic equation.