Sensitivity and chaos on product and on hyperspatial semiflows

Thakur, Rahul; Das, Ruchi

doi:10.1080/10236198.2020.1862807

Cited by 10 publications

(5 citation statements)

References 22 publications

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“…The presence of continuous unpredictable oscillations in various types of differential equations was demonstrated in the studies [15]- [17]. Moreover, the reader is referred to the papers [20]- [22] for generalizations of Poincaré chaos and unpredictable points to topological spaces.…”

Section: Introductionmentioning

confidence: 94%

Unpredictability in Perturbed Quasilinear Systems with Regular Moments of Impulses

Fen¹,

Fen²

2021

Preprint

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It is rigorously proved that quasilinear impulsive systems possess unpredictable solutions when a perturbation generated by an unpredictable sequence is applied. The existence, uniqueness, as well as asymptotic stability of such solutions are demonstrated. The system under consideration is with regular moments of impulses, and for that reason a novel definition for unpredictable functions with regular discontinuity moments is provided. To show the existence of an unpredictable solution a Gronwall type inequality for piecewise continuous functions is utilized. The theoretical results are supported with an illustrative example.

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Section: Introductionmentioning

confidence: 94%

Unpredictability in Perturbed Quasilinear Systems with Regular Moments of Impulses

Fen¹,

Fen²

2021

Preprint

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“…Additionally, Thakur and Das [7] studied Poincaré chaos on the product of semiflows. Moreover, the presence of an unpredictable point in an hyperspatial semiflow was demonstrated in [8].…”

Section: Introductionmentioning

confidence: 98%

“…Additionally, the paper [4] was devoted to the existence and uniqueness of unpredictable solutions in systems with delay. The papers [6]- [8], on the other hand, are concerned with Poincaré chaos in topological spaces. The concept of unpredictable point was generalized to semiflows with arbitrary acting topological monoids by Miller [6].…”

Section: Introductionmentioning

confidence: 99%

Unpredictable Solutions of Quasilinear Systems with Discontinuous Right-Hand Sides

Fen¹,

Fen²

2021

Preprint

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It is rigorously proved under certain assumptions that a quasilinear system with discontinuous righthand side possesses a unique unpredictable solution. The discontinuous perturbation function on the right-hand side is defined by means of an unpredictable sequence. A Gronwall-Coppel type inequality is utilized to achieve the main result, and the stability of the unpredictable solution is discussed. Examples with exponentially asymptotically stable and unstable unpredictable solutions are provided.

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“…Interesting results concerning unpredictable motions as well as Poincaré chaos in topological spaces were provided in papers [5]- [7]. Miller [5] generalized the notion of unpredictable points to the case of semiflows with arbitrary acting abelian topological monoids, whereas Thakur and Das [6] demonstrated that at least one of the factors is Poincaré chaotic provided that the same is true for finite or countably infinite products of semiflows.…”

Section: Introductionmentioning

confidence: 99%

A Novel Criterion for Unpredictable Motions

Fen¹,

Fen²,

Akhmet³

2022

Preprint

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We demonstrate the extension of unpredictable motions in coupled autonomous systems with skew product structure in the case that generalized synchronization takes place. Sufficient conditions for the existence of unpredictable motions in the dynamics of the response system are provided. The theoretical results are exemplified for coupled autonomous systems in which the drive is a hybrid dynamical system and the response is a Lorenz system. The auxiliary system approach and conditional Lyapunov exponents are utilized to detect the presence of generalized synchronization.

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Sensitivity and chaos on product and on hyperspatial semiflows

Cited by 10 publications

References 22 publications

Unpredictability in Perturbed Quasilinear Systems with Regular Moments of Impulses

Unpredictability in Perturbed Quasilinear Systems with Regular Moments of Impulses

Unpredictable Solutions of Quasilinear Systems with Discontinuous Right-Hand Sides

A Novel Criterion for Unpredictable Motions

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