Unpredictable solutions of linear differential and discrete equations

Date

2019-01-01

Author

Akhmet, Marat
Tleubergenova, Madina
Zhamanshin, Akylbek

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

213
views

0
downloads

The existence and uniqueness of unpredictable solutions in the dynamics of nonhomogeneous linear systems of differential and discrete equations are investigated. The hyperbolic cases are under discussion. The presence of unpredictable solutions confirms the existence of Poincare chaos. Simulations illustrating the chaos are provided.

Subject Keywords

Unpredictable solutions, Poincare chaos, linear nonhomogeneous systems

URI

https://hdl.handle.net/11511/45734

Journal

TURKISH JOURNAL OF MATHEMATICS

DOI

https://doi.org/10.3906/mat-1810-86

Collections

Department of Mathematics, Article

Suggestions

OpenMETU
Core

Quasilinear differential equations with strongly unpredictable solutions Akhmet, Marat; Zhamanshin, Akylbek (2020-01-01) The authors discuss the existence and uniqueness of asymptotically stable unpredictable solutions for some quasilinear differential equations. Two principal novelties are in the basis of this research. The first one is that all coordinates of the solution are unpredictable functions. That is, solutions are strongly unpredictable. Secondly, perturbations are strongly unpredictable functions in the time variable. Examples with numerical simulations are presented to illustrate the theoretical results.
Almost periodic solutions of the linear differential equation with piecewise constant argument Akhmet, Marat (2009-10-01) The paper is concerned with the existence and stability of almost periodic solutions of linear systems with piecewise constant argument where t∈R, x ∈ Rn [·] is the greatest integer function. The Wexler inequality [1]-[4] for the Cauchy's matrix is used. The results can be easily extended for the quasilinear case. A new technique of investigation of equations with piecewise argument, based on an integral representation formula, is proposed. Copyright © 2009 Watam Press.
Dynamics of numerical methods for cosymmetric ordinary differential equations Govorukhin, VN; Tsybulin, VG; Karasözen, Bülent (2001-09-01) The dynamics of numerical approximation of cosymmetric ordinary differential equations with a continuous family of equilibria is investigated. Nonconservative and Hamiltonian model systems in two dimensions are considered and these systems are integrated with several first-order Runge-Kutta methods. The preservation of symmetry and cosymmetry, the stability of equilibrium points, spurious solutions and transition to chaos are investigated by presenting analytical and numerical results. The overall performan...
Unpredictable solutions of quasilinear differential equations with generalized piecewise constant arguments of mixed type Tleubergenova, Madina; Çinçin, Duygu Aruğaslan; Nugayeva, Zakhira; Akhmet, Marat (2023-01-01) An unpredictable solution is found for a quasilinear differential equation with generalized piece-wise constant argument (EPCAG). Sufficient conditions are provided for the existence, uniqueness and exponential stability of the unpredictable solution. The theoretical results are confirmed by examples and illustrated by simulations.
Multi-symplectic integration of coupled non-linear Schrodinger system with soliton solutions AYDIN, AYHAN; Karasözen, Bülent (2009-01-01) Systems of coupled non-linear Schrodinger equations with soliton solutions are integrated using the six-point scheme which is equivalent to the multi-symplectic Preissman scheme. The numerical dispersion relations are studied for the linearized equation. Numerical results for elastic and inelastic soliton collisions are presented. Numerical experiments confirm the excellent conservation of energy, momentum and norm in long-term computations and their relations to the qualitative behaviour of the soliton sol...

Citation Formats

M. Akhmet, M. Tleubergenova, and A. Zhamanshin, “Unpredictable solutions of linear differential and discrete equations,” TURKISH JOURNAL OF MATHEMATICS, pp. 2377–2389, 2019, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/45734.