Quasilinear differential equations with strongly unpredictable solutions

Akhmet, Marat
Zhamanshin, Akylbek
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.


Unpredictable solutions of linear differential and discrete equations
Akhmet, Marat; Tleubergenova, Madina; Zhamanshin, Akylbek (2019-01-01)
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.
Akhmet, Marat (2014-03-01)
We introduce a new class of differential equations, retarded differential equations with functional dependence on piecewise constant argument, RFDEPCA, and focus on quasilinear systems. Formulation of the initial value problem, bounded solutions, periodic and almost periodic solutions, their stability are under investigation. Illustrating examples are provided.
Almost periodic solutions of second order neutral differential equations with functional response on piecewise constant argument
Akhmet, Marat (2013-01-01)
© 2013 L & H Scientific Publishing, LLC.We consider second order functional differential equations with generalized piecewise constant argument. Conditions for existence, uniqueness and stability of Bohr almost periodic solutions are defined. Appropriate examples which illustrate the results are provided.
Differential - Operator solutions for complex partial differential equations
Celebi, O; Sengul, S (1998-07-10)
The solutions of complex partial differential equations of order four are obtained by using polynomial differential operators. A correspondence principle is also derived for the solutions of two different differential equations, imposing conditions on the coefficients.
Strongly unpredictable solutions of difference equations
Akhmet, Marat; Tleubergenova, M.; Zhamanshin, A. (2019-01-01)
It so happens that the line of oscillations in the classical theory of dynamical systems, which is founded by H.Poincar'e and G.Birkhoff was broken at Poisson stable motions. The next oscillations were considered as actors of chaotic processes. This article discusses the new type of oscillations, unpredictable sequences, the presence of which proves the existence of Poincare chaos. The sequence is defined as an unpredictable function on the set of integers. The results continue the description of chaos whic...
Citation Formats
M. Akhmet and A. Zhamanshin, “Quasilinear differential equations with strongly unpredictable solutions,” CARPATHIAN JOURNAL OF MATHEMATICS, pp. 341–349, 2020, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/54473.