scholarly journals On some kinds of dense orbits in general nonautonomous dynamical systems

2020 ◽  
Vol 7 (1) ◽  
pp. 163-175
Author(s):  
Mehdi Pourbarat
Keyword(s):  
Dynamical Systems ◽  
Initial Conditions ◽  
Point Of View ◽  
Topological Conjugacy ◽  
Topological Transitivity ◽  
Nonautonomous Systems ◽  
Nonautonomous Dynamical Systems ◽  
Sensitive Dependence ◽  
Dense Orbits

AbstractWe study the theory of universality for the nonautonomous dynamical systems from topological point of view related to hypercyclicity. The conditions are provided in a way that Birkhoff transitivity theorem can be extended. In the context of generalized linear nonautonomous systems, we show that either one of the topological transitivity or hypercyclicity give sensitive dependence on initial conditions. Meanwhile, some examples are presented for topological transitivity, hypercyclicity and topological conjugacy.

Sensitivity of Nonautonomous Dynamical Systems on Uniform Spaces

2021 ◽  
Vol 31 (01) ◽  
pp. 2150017
Author(s):  
Mohammad Salman ◽  
Xinxing Wu ◽  
Ruchi Das
Keyword(s):  
Dynamical Systems ◽  
Sufficient Conditions ◽  
Periodic Points ◽  
Uniform Spaces ◽  
Topological Transitivity ◽  
Nonautonomous Systems ◽  
Nonautonomous Dynamical Systems

We introduce the concepts of sensitivity, multisensitivity, cofinite sensitivity, and syndetic sensitivity for nonautonomous dynamical systems on uniform spaces and obtain some sufficient conditions under which topological transitivity and dense periodic points imply sensitivity for nonautonomous systems on Hausdorff uniform spaces. We also study sensitivity and other stronger versions of sensitivity for the systems induced on hyperspaces and for the product of nonautonomous dynamical systems on uniform spaces.

On the dynamics of the Tent function - Phase diagrams

2016 ◽  
Vol 7 (4) ◽  
pp. 261
Author(s):  
Prince Amponsah Kwabi ◽  
William Obeng Denteh ◽  
Richard Kena Boadi
Keyword(s):  
Dynamical Systems ◽  
Phase Diagrams ◽  
Initial Conditions ◽  
Asymptotic Properties ◽  
Topological Dynamical System ◽  
Topological Transitivity ◽  
Tent Map ◽  
One Dimensional ◽  
Definition Of ◽  
Topological Dynamical Systems

This paper focuses on the study of a one-dimensional topological dynamical system, the tent function. We give a good background to the theory of dynamical systems while establishing the important asymptotic properties of topological dynamical systems that distinguishes it from other fields by way of an example - the tent function. A precise definition of the tent function is given and iterates are clearly shown using the phase diagrams. By this same method, chaos in the tent map is shown as iterates become higher. We also show that the tent map has infinitely many chaotic orbits and also express some important features of chaos such as topological transitivity, boundedness and sensitivity to change in initial conditions from a topological viewpoint.

scholarly journals Unpredicted Trajectories of an Automated Guided Vehicle with Chaos

Robotics ◽  
2013 ◽  
pp. 1012-1019
Author(s):  
Magda Judith Morales Tavera ◽  
Omar Lengerke ◽  
Max Suell Dutra
Keyword(s):  
Mobile Robot ◽  
Intelligent Transportation Systems ◽  
Vehicular Networks ◽  
Initial Conditions ◽  
Transportation Systems ◽  
Automated Guided Vehicle ◽  
Topological Transitivity ◽  
Chaotic Motions ◽  
Sensitive Dependence ◽  
Scanning Motion

Intelligent Transportation Systems (ITS) are the future of transportation. As a result of emerging standards, vehicles will soon be able to talk to one another as well as their environment. A number of applications will be made available for vehicular networks that improve the overall safety of the transportation infrastructure. This chapter develops a method to impart chaotic motions to an Automated Guided Vehicle (AGV). The chaotic AGV implies a mobile robot with a controller that ensures chaotic motions. This kind of motion is characterized by the topological transitivity and the sensitive dependence on initial conditions. Due the topological transitivity, the mobile robot is guaranteed to scan the whole connected workspace. For scanning motion, the chaotic robot neither requires a map of the workspace nor plans global motions. It only requires the measurement of the workspace boundary when it comes close to it.

scholarly journals Dweiltime Analysis of Symmetry-Breaking Dynamical Systems

1995 ◽  
Vol 50 (12) ◽  
pp. 1117-1122 ◽  
Author(s):  
J. Vollmer ◽  
J. Peinke ◽  
A. Okniński
Keyword(s):  
Dynamical Systems ◽  
Symmetry Breaking ◽  
Dwell Time ◽  
Initial Conditions ◽  
Dissipative Systems ◽  
Time Analysis ◽  
Chaotic Scattering ◽  
One Dimensional ◽  
Basin Boundary ◽  
Sensitive Dependence

Abstract Dweiltime analysis is known to characterize saddles giving rise to chaotic scattering. In the present paper it is used to characterize the dependence on initial conditions of the attractor approached by a trajectory in dissipative systems described by one-dimensional, noninvertible mappings which show symmetry breaking. There may be symmetry-related attractors in these systems, and which attractor is approached may depend sensitively on the initial conditions. Dwell-time analysis is useful in this context because it allows to visualize in another way the repellers on the basin boundary which cause this sensitive dependence.

Analyzing Devaney Chaos of a Sine–Cosine Compound Function System

2018 ◽  
Vol 28 (14) ◽  
pp. 1850176 ◽  
Author(s):  
Hegui Zhu ◽  
Wentao Qi ◽  
Jiangxia Ge ◽  
Yuelin Liu
Keyword(s):  
Chaotic Behavior ◽  
Initial Conditions ◽  
Function System ◽  
Topological Transitivity ◽  
One Dimensional ◽  
Devaney’S Chaos ◽  
Chebyshev Map ◽  
Sensitive Dependence ◽  
Sine Map ◽  
The One

The one-dimensional Sine map and Chebyshev map are classical chaotic maps, which have clear chaotic characteristics. In this paper, we establish a chaotic framework based on a Sine–Cosine compound function system by analyzing the existing one-dimensional Sine map and Chebyshev map. The sensitive dependence on initial conditions, topological transitivity and periodic-point density of this chaotic framework is proved, showing that the chaotic framework satisfies Devaney’s chaos definition. In order to illustrate the chaotic behavior of the chaotic framework, we propose three examples, called Cosine–Polynomial (C–P) map, Sine–Tangent (S–T) map and Sine–Exponent (S–E) map, respectively. Then, we evaluate the chaotic behavior with Sine map and Chebyshev map by analyzing bifurcation diagrams, Lyapunov exponents, correlation dimensions, Kolmogorov entropy and [Formula: see text] complexity. Experimental results show that the chaotic framework has better unpredictability and more complex chaotic behaviors than the classical Sine map and Chebyshev map. The results also verify the effectiveness of the theoretical analysis of the proposed chaotic framework.

Unpredicted Trajectories of an Automated Guided Vehicle with Chaos

2012 ◽  
pp. 318-325
Author(s):  
Magda Judith Morales Tavera ◽  
Omar Lengerke ◽  
Max Suell Dutra
Keyword(s):  
Mobile Robot ◽  
Intelligent Transportation Systems ◽  
Vehicular Networks ◽  
Initial Conditions ◽  
Transportation Systems ◽  
Automated Guided Vehicle ◽  
Topological Transitivity ◽  
Chaotic Motions ◽  
Sensitive Dependence ◽  
Scanning Motion

Intelligent Transportation Systems (ITS) are the future of transportation. As a result of emerging standards, vehicles will soon be able to talk to one another as well as their environment. A number of applications will be made available for vehicular networks that improve the overall safety of the transportation infrastructure. This chapter develops a method to impart chaotic motions to an Automated Guided Vehicle (AGV). The chaotic AGV implies a mobile robot with a controller that ensures chaotic motions. This kind of motion is characterized by the topological transitivity and the sensitive dependence on initial conditions. Due the topological transitivity, the mobile robot is guaranteed to scan the whole connected workspace. For scanning motion, the chaotic robot neither requires a map of the workspace nor plans global motions. It only requires the measurement of the workspace boundary when it comes close to it.

scholarly journals Research on a Dynamic Master-Slave Cournot Triopoly Game Model with Bounded Rational Rule and Its Control

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Hongliang Tu ◽  
Xinyu Wang
Keyword(s):  
Dynamical Systems ◽  
Phase Portrait ◽  
Bifurcation Theory ◽  
Initial Conditions ◽  
Stable Region ◽  
Game Model ◽  
Dynamical Behaviors ◽  
Sensitive Dependence ◽  
Adjustment Speed ◽  
Largest Lyapunov Exponents

The oligopoly market is modelled by a new dynamic master-slave Cournot triopoly game model with bounded rational rule. The local stabile conditions and the stable region are got by the dynamical systems bifurcation theory. The dynamics characteristics of the system with the changes of the adjustment speed parameters are analyzed by means of bifurcation diagram, largest Lyapunov exponents, phase portrait, and sensitive dependence on initial conditions. Furthermore, the parameters adjustment method is used to control the complex dynamical behaviors of the systems. The derived results have some important theoretical and practical meanings for the oligopoly market.

scholarly journals A Study of Chaos in Dynamical Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-5 ◽  
Author(s):  
S. Effah-Poku ◽  
W. Obeng-Denteh ◽  
I. K. Dontwi
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Fixed Points ◽  
Initial Conditions ◽  
Period Doubling ◽  
Dense Orbit ◽  
Routes To Chaos ◽  
Sensitive Dependence ◽  
Nonlinear Science

The behavior of systems such as periodicity, fixed points, and most importantly chaos has evolved as an integral part of mathematics, especially in dynamical system. This research presents a study on chaos as a property of nonlinear science. Systems with at least two of the following properties are considered to be chaotic in a certain sense: bifurcation and period doubling, period three, transitivity and dense orbit, sensitive dependence to initial conditions, and expansivity. These are termed as the routes to chaos.

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