Abstract
This chapter is concerned with the existence and uniqueness of asymptotically stable unpredictable solutions for quasilinear differential equations. Two principal novelties are in the basis of the research. The first one is that all coordinates of a solution are unpredictable functions. That is, solutions are strongly unpredictable. Second, perturbations are strongly unpredictable in the time variable functions. Examples with numerical simulations are presented to illustrate the theoretical results. The results of this chapter are published in the paper.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
M. Akhmet, M.O. Fen, Existence of unpredictable solutions and chaos. Turk. J. Math. 41, 254–266 (2017)
M. Akhmet, M.O. Fen, Poincaré chaos and unpredictable functions. Commun. Nonlinear Sci. Numer. Simul. 48, 85–94 (2017)
M. Akhmet, M.O. Fen, Non-autonomous equations with unpredictable solutions. Commun. Nonlinear Sci. Numer. Simul. 59, 657–670 (2018)
M. Akhmet, M.O. Fen, M. Tleubergenova, A. Zhamanshin, Poincaré chaos for a hyperbolic quasilinear system. Miskolc Math. Notes 20, 33–44 (2019)
M. Akhmet, M. Tleubergenova, A. Zhamanshin, Quasilinear differential equations with strongly unpredictable solutions. Carpathian J. Math. (in press)
H.A. Bohr, Almost Periodic Functions (Chelsea Publishing Company, 1947)
C. Corduneanu, Almost Periodic Oscillations and Waves (Springer, Berlin, 2009)
M. Farkas, Periodic Motions (Springer, New York, 1994)
A.M. Fink, Almost Periodic Differential Equations (Springer, New York, 1974)
P. Hartman, Ordinary Differential Equations (SIAM, New York, 2002)
Y. Hino, T. Naito, N. VanMinh, J.S. Shin, Almost Periodic Solutions of Differential Equations in Banach Spaces (CRC Press, 2001)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Akhmet, M., Fen, M.O., Alejaily, E.M. (2020). Strongly Unpredictable Solutions. In: Dynamics with Chaos and Fractals. Nonlinear Systems and Complexity, vol 29. Springer, Cham. https://doi.org/10.1007/978-3-030-35854-9_7
Download citation
DOI: https://doi.org/10.1007/978-3-030-35854-9_7
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-35853-2
Online ISBN: 978-3-030-35854-9
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)