Li–Yorke Chaos in Hybrid Systems on a Time Scale

DOI10.1142/S0218127415400246zbMath1334.37028arXiv1505.04453MaRDI QIDQ2800663

Mehmet Onur Fen, Marat U. Akhmet

Publication date: 18 April 2016

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1505.04453

zbMATH Keywords

hybrid systemsDuffing equationLi-Yorke chaosproximalitydynamic equations on time scalesfrequent separation

Mathematics Subject Classification ID

Transformation and reduction of ordinary differential equations and systems, normal forms (34C20) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45) Dynamic equations on time scales or measure chains (34N05)

Related Items (2)

Homoclinic and Heteroclinic Motions in Economic Models with Exogenous Shocks ⋮ Existence of positive solutions for nonlinear third-order \(m\)-point impulsive boundary-value problems on time scales

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Chaotic period-doubling and OGY control for the forced Duffing equation
• Periodic solution of single population models on time scales
• Devaney's chaos of a relay system
• The differential equations on time scales through impulsive differential equations
• Hybrid systems with time scales and impulses
• Basic qualitative and quantitative results for solutions to nonlinear dynamic equations on time scales with an application to economic modelling
• Chaos of discrete dynamical systems in complete metric spaces
• Replication of chaos
• Li-Yorke chaos in a spatiotemporal chaotic system
• Li and Yorke chaos with respect to the cardinality of the scrambled sets
• Li-Yorke chaos in the system with impacts
• Differential equations on variable time scales
• Macro- and micro-chaotic structures in the Hindmarsh-Rose model of bursting neurons
• DYNAMICAL SYNTHESIS OF QUASI-MINIMAL SETS
• Period Three Implies Chaos
• FROM ALMOST PERIODIC TO CHAOTIC: THE FUNDAMENTAL MAP
• DYNAMICAL SYNTHESIS OF POINCARÉ MAPS
• Chaos: Generating Complexity from Simplicity
• On Li-Yorke pairs
• HYPERCHAOS IN A MODIFIED CANONICAL CHUA'S CIRCUIT
• Toward Analytical Chaos in Nonlinear Systems
• Establishing the Onset, and Parameter and Spatial Domains, of Chaos in a Smooth Quadratic Autonomous System Using Sil’nikov Criteria and Competitive Modes Analysis
• CHAOS AND COMPLEXITY
• Li–Yorke chaos in higher dimensions: a review
• LI-Yorke sensitivity and other concepts of chaos
• On Non-Linear Differential Equations of the Second Order: I. the Equation y¨ − k (1-y ² )y˙ + y = b λk cos(λl + α), k Large

This page was built for publication: Li–Yorke Chaos in Hybrid Systems on a Time Scale