[PDF] Top 20 Stability of Difference Equations and Applications to Robustness Problems

... dynamic equations on time scales see 35, 36, having a wide potential for applications in the study of population ...difference equations, which often proceed from the linearization of nonlinear ... See full document

... that stability is one of the basic problems in various dynamical ...the stability theory of difference equations are presented, for example, by Agarwal [], Elaydi [], Halanay and Rasvan [], ... See full document

... [5] X. Yang, D. J. Evans, and G. M. Megson, “Global asymptotic stability in a class of Putnam-type equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 64, no. 1, pp. 42–50, 2006. ... See full document

... Nonlinear Difference Equations, Chapman & Hall/CRC, ...Global stability in some population models, in Proceedings of the 4th International Conference on Difference Equations and ... See full document

... , stability estimates for the solution of this problem are ...In applications, two mixed problems for tele- graph partial differential equations are ...presented. Stability estimates ... See full document

... Ulam–Hyers–Rassias stability results for a class of implicit fractional q-difference ...Some applications are made of some fixed point theorems in Banach spaces for the existence and uniqueness of solutions, ... See full document

... of stability of nonlinear difference equations with delays has attracted a lot of attention from many researchers such as Agarwal et ...the stability theory of linear systems with ...new ... See full document

... For applications and details on fractional calculus, we refer the readers to ...Such equations arise in management sciences, business mathematics and other managerial sciences, and so ...such ... See full document

... successful applications of nonlinear analysis and classical fixed point theory, we have developed adequate conditions under which the proposed class of implicit impulsive FODEs has at least one ...nonlinear ... See full document

... of stability problems for functional equations is related to a question of Ulams[24] concerning the stability of group homomorphism’s was affirmatively answered for Banach spaces by ... See full document

... differential equations. Realizing that most of the problems that arise in practice are nonlinear and mostly unsolvable, the qualitative behaviors of solutions without actually computing them are of vital ... See full document

... Hyers-Ulam stability of the first-order matrix difference equations has been proved in [] in a general ...the stability problems for the ‘backward’ difference equations have been treated ... See full document

... Notice that in the applications given in Section 3, by virtue of the choice of the vec- tor function G, both systems in (3.8) and in (3.25) are linear and nonhomogeneous and the conditions (b) and (c) of Theorem ... See full document

... difference equations (IDEs) arise in various applications, such as the Leontief dynamic model of a multisector economy, the Leslie population growth model, and so ...algebraic equations (DAEs) which ... See full document

... the rotation-controlling magnitude of ρ. It shows that both noise and rotation terms have to be chosen carefully in order not to destabilize the long-term dynamics by partially drift-implicit θ-methods (4.2). Anyway, ... See full document

... It is well known that the term ‘elliptic boundary value problem’ means not only satisfying certain equation in inner points of a manifold, but satisfying some boundary conditions as well. But it is not enough. These ... See full document

... condition 4.12 holds 4 ∈ −∞, −0.2 ∪ 3.2, ∞ and therefore the equilibrium point x 3 is stable: all trajectories go to x. Putting σ 0.9, we obtain that stability condition 4.12 does not hold 4 / ∈ −∞, −1.78 ∪ 4.78, ... See full document

... Hindawi Publishing Corporation Advances in Difference Equations Volume 2011, Article ID 782057, 11 pages doi 10 1155/2011/782057 Research Article Annular Bounds for Polynomial Zeros and Schur Stabilit[.] ... See full document

... is exponentially stable, since |0.50.1 sin n||0.6−0.1 sin n| 1.1 and 0.7·1.1|1−1.1| 0.87 < 1. Now let us assume that all coefficients are proportional. Such equations arise as linear approximations of nonlinear ... See full document

... A biological system is a nonlinear system, so it is still a public problem upon how to con- trol the biological system balance. The predecessors have done a lot of research. Especially the research on the predator-prey ... See full document