Topological entropy of composition and impulsive differential equations satisfying a uniqueness condition

2022 ◽  
Vol 156 ◽  
pp. 111800
Jan Andres ◽  
Pavel Ludvík
Mathematics ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1602
Jan Andres ◽  
Jerzy Jezierski

The main aim of this article is two-fold: (i) to generalize into a multivalued setting the classical Ivanov theorem about the lower estimate of a topological entropy in terms of the asymptotic Nielsen numbers, and (ii) to apply the related inequality for admissible pairs to impulsive differential equations and inclusions on tori. In case of a positive topological entropy, the obtained result can be regarded as a nontrivial contribution to deterministic chaos for multivalued impulsive dynamics.

2021 ◽  
Vol 31 (07) ◽  
pp. 2150113
Jan Andres

The deterministic chaos in the sense of a positive topological entropy is investigated for differential equations with multivalued impulses. Two definitions of topological entropy are examined for three classes of multivalued maps: [Formula: see text]-valued maps, [Formula: see text]-maps and admissible maps in the sense of Górniewicz. The principal tool for its lower estimates and, in particular, its positivity are the Ivanov-type inequalities in terms of the asymptotic Nielsen numbers. The obtained results are then applied to impulsive differential equations via the associated Poincaré translation operators along their trajectories. The main theorems for chaotic differential equations with multivalued impulses are formulated separately on compact subsets of Euclidean spaces and on tori. Several illustrative examples are supplied.

Symmetry ◽  
2021 ◽  
Vol 13 (3) ◽  
pp. 501
Ahmed Boudaoui ◽  
Khadidja Mebarki ◽  
Wasfi Shatanawi ◽  
Kamaleldin Abodayeh

In this article, we employ the notion of coupled fixed points on a complete b-metric space endowed with a graph to give sufficient conditions to guarantee a solution of system of differential equations with impulse effects. We derive recisely some new coupled fixed point theorems under some conditions and then apply our results to achieve our goal.

2021 ◽  
Vol 2021 (1) ◽  
Shyam Sundar Santra ◽  
Apurba Ghosh ◽  
Omar Bazighifan ◽  
Khaled Mohamed Khedher ◽  
Taher A. Nofal

AbstractIn this work, we present new necessary and sufficient conditions for the oscillation of a class of second-order neutral delay impulsive differential equations. Our oscillation results complement, simplify and improve recent results on oscillation theory of this type of nonlinear neutral impulsive differential equations that appear in the literature. An example is provided to illustrate the value of the main results.

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