SHADOWING AND DYNAMICAL SYNTHESIS

2009-10-01
We discuss a system with a discontinuity moments generator to obtain the solutions. It is proven that the system is chaotic and has shadowing property [Anosov, 1967; Bowen, 1975; Hammel et al., 1987; Robinson, 1995] if the generator possesses these characteristics. Illustrative examples are provided.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS

Suggestions

Bifurcation of a non-smooth planar limit cycle from a vertex
Akhmet, Marat (2009-12-15)
We investigate non-smooth planar systems of differential equations with discontinuous right-hand sides. Discontinuity sets intersect at a vertex, and are of quasilinear nature. By means of the B-equivalence method, which was introduced in [M. Akhmetov, Asymptotic representation of solutions of regularly perturbed systems of differential equations with a nonclassical right-hand side, Ukrainian Math. J. 43 (1991) 1209-1214; M. Akhmetov, On the expansion of solutions to differential equations with discontinuou...
Signaling Games for Log-Concave Distributions: Number of Bins and Properties of Equilibria
Kazikli, Ertan; Sarıtaş, Serkan; GEZİCİ, Sinan; Linder, Tamas; Yuksel, Serdar (2022-03-01)
We investigate the equilibrium behavior for the decentralized cheap talk problem for real random variables and quadratic cost criteria in which an encoder and a decoder have misaligned objective functions. In prior work, it has been shown that the number of bins in any equilibrium has to be countable, generalizing a classical result due to Crawford and Sobel who considered sources with density supported on [0, 1]. In this paper, we first refine this result in the context of log-concave sources. For sources ...
Parallel preconditioners for solutions of dense linear systems with tens of millions of unknowns
Malas, Tahir; Ergül, Özgür Salih; Gurel, Levent (2007-11-09)
We propose novel parallel preconditioning schemes for the iterative solution of integral equation methods. In particular, we try to improve convergence rate of the ill-conditioned linear systems formulated by the electric-field integral equation, which is the only integral-equation formulation for targets having open surfaces. For moderate-size problems, iterative solution of the neat-field system enables much faster convergence compared to the widely used sparse approximate inverse preconditioner. For larg...
Matrix measure approach to Lyapunov-type inequalities for linear Hamiltonian systems with impulse effect
Kayar, Zeynep; Zafer, Ağacık (Elsevier BV, 2016-08-01)
We present new Lyapunov-type inequalities for Hamiltonian systems, consisting of 2n-first-order linear impulsive differential equations, by making use of matrix measure approach. The matrix measure estimates of fundamental matrices of linear impulsive systems are crucial in obtaining sharp inequalities. To illustrate usefulness of the inequalities we have derived new disconjugacy criteria for Hamiltonian systems under impulse effect and obtained new lower bound estimates for eigenvalues of impulsive eigenva...
Devaney's chaos of a relay system
Akhmet, Marat (2009-04-01)
We address the differential equation with a pulse function, whose moments of discontinuity depend on the initial moment. The existence of a chaotic attractor, and the complex behavior of all solutions are investigated. An appropriate simulations are presented.
Citation Formats
M. Akhmet, “SHADOWING AND DYNAMICAL SYNTHESIS,” INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, pp. 3339–3346, 2009, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/38975.