[PDF] Top 20 Variationally stable dynamic systems on time scales

... linear dynamic equa- tions on time scales by using the unified time scale quadratic Lyapunov ...linear time-varying system with nonlinear perturbation on time scales by ... See full document

... periodic systems on time scales, we establish LaSalle stationary oscillation theorem to obtain the existence and asymptotic stability of affine periodic solutions on time ...on time ... See full document

... arbitrary time scale. We consider continuous- and discrete-time models and also models on time scales simultaneously consisting of both kinds of points, right-dense and ... See full document

... the delay functions. We are interested in the asymptotic behavior of solutions of the mentioned system. More precisely, we formulate conditions on a function f, which guarantee that the graph of at least one solution of ... See full document

... on time scales and then formulate appropriate inequal- ities on these functions that guarantee that the trivial solution to ...exponentially stable on [0, ∞ ... See full document

... The paper is organized as follows. In the next section we recall some basic notions and preliminary results on time scales and deal with the solvability of IDEs. In Section 3, we prove that if the system ... See full document

... f t ∞ × R → R is a rd-continuous function, T is a time scales. In this paper, we shall investigate some results for the exponential stability of the dynamic Equation (1) by combinating the first ... See full document

... of dynamic equations on a time scale goes back to Aulbach and Hilger ...scalar dynamic equation, stability and instability results were obtained by Gard and Hoffacker ...for time-varying ... See full document

... predator-prey dynamic systems on time scales calculus are ...predator-prey dynamic systems with Beddington-DeAngelis type functional ...are time scales cal- culus ... See full document

... Fluctuation analysis Keeling et al., 1997 and determinism tests Pascual and Levin, 1999 for estimating CLSs are attractive because they are appropriate to the complicated dynamics of som[r] ... See full document

... To our knowledge, in this paper, we establish the first multiplicity result for the system (.). In order to obtain the existence of at least three solutions of (.), we introduce the notion of a strict solution-tube of ... See full document

... dynamical systems have a number of significant differences mainly due to the topological fact that in one case the time scale T R, real numbers, and the corresponding trajectories are connected while in ... See full document

... linear dynamic systems with a small parameter ε on a time scale unifying continuous and discrete WKB ...2 dynamic system on a time scale, which is a generalization of adiabatic ... See full document

... The problem of controllability to a given convex target set of a linear time-varying control system on time scales is studied. Necessary and sufficient conditions of controllability with constrained ... See full document

... for dynamic equations on time scales, which generalize the corresponding results on differential and difference ...Hamiltonian systems can be obtained by Lyapunov-type inequalities and Flo- ... See full document

... Existence results for system (1.2) were obtained in [5] with f is a continuous function. In the particular case where n = 1, existence results for first-order ∇-dynamic equation on time scales were ... See full document

... of dynamic equations on time scales, which follows Hilger’s landmark paper [], is a new study area of mathematics that has received a lot of ...for dynamic equations on time ... See full document

... We assume that T has the topology that it inherits from the standard topology on the real numbers R. The forward and the backward jump operators on any time scale T are defined by σ(t) := inf { s ∈ T : s > t } , ... See full document

... ous results of the first author (and his co-authors) concerning the asymptotic behavior of solutions of discrete equations; see, e.g., [–]. In papers [, ], in our best knowledge, the retract principle is extended to ... See full document

... We get the unique Steffensen inequalities by utilizing the diamond-α integrals on time scales. For α = 1, the diamond-α integral moves toward becoming delta integral and for α = 0 it moves toward becoming ... See full document