Curry–Yorke route to shearless attractors and coexistence of attractors in dissipative nontwist systems

2021 ◽  
Vol 31 (2) ◽  
pp. 023125
Author(s):  
Michele Mugnaine ◽  
Antonio M. Batista ◽  
Iberê L. Caldas ◽  
José D. Szezech ◽  
Ricardo Egydio de Carvalho ◽  
...  
Keyword(s):  
Coexistence Of Attractors

scholarly journals Complex Dynamical Behaviors of a Mixed Duopoly Game Based on Intellectual Property Rights Protection

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Tong Chu ◽  
Yu Yu ◽  
Xiaoxue Wang
Keyword(s):  
Intellectual Property ◽  
Property Rights ◽  
Intellectual Property Rights ◽  
Mixed Duopoly ◽  
Fractal Structures ◽  
Rights Protection ◽  
Intellectual Property Rights Protection ◽  
Dynamical Behaviors ◽  
Property Rights Protection ◽  
Coexistence Of Attractors

Based on the oligopoly game theory and the intellectual property rights protection policy, we investigate the complex dynamical behaviors of a mixed duopoly game with quadratic cost. In the new system, a few parameters are improved by considering intellectual property rights protection and the stability conditions of the Nash equilibrium point are discussed in detail. A set of the two-dimensional bifurcation diagrams is demonstrated by using numerical modeling, and these diagrams show abundant complex dynamical behaviors, such as coexistence of attractors, different bifurcation, and fractal structures. These dynamical properties can present the long-run effects of strengthening intellectual property protection.

Coexistence of attractors in autonomous Van der Pol–Duffing jerk oscillator: Analysis, chaos control and synchronisation in its fractional-order form

Pramana ◽  
2018 ◽  
Vol 91 (1) ◽  
Author(s):  
Victor Kamdoum Tamba ◽  
Sifeu Takougang Kingni ◽  
Gaetan Fautso Kuiate ◽  
Hilaire Bertrand Fotsin ◽  
Pierre Kisito Talla
Keyword(s):  
Fractional Order ◽  
Chaos Control ◽  
Van Der Pol ◽  
Order Form ◽  
Coexistence Of Attractors

scholarly journals Autonomous Jerk Oscillator with Cosine Hyperbolic Nonlinearity: Analysis, FPGA Implementation, and Synchronization

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Sifeu Takougang Kingni ◽  
Gaetan Fautso Kuiate ◽  
Victor Kamdoum Tamba ◽  
Viet-Thanh Pham
Keyword(s):  
Control Method ◽  
Sliding Mode ◽  
Equilibrium Points ◽  
Period Doubling ◽  
Fpga Implementation ◽  
Phase Portraits ◽  
Adaptive Sliding Mode Control ◽  
Coexistence Of Attractors ◽  
Route To Chaos ◽  
Two Parameters

A two-parameter autonomous jerk oscillator with a cosine hyperbolic nonlinearity is proposed in this paper. Firstly, the stability of equilibrium points of proposed autonomous jerk oscillator is investigated by analyzing the characteristic equation and the existence of Hopf bifurcation is verified using one of the two parameters as a bifurcation parameter. By tuning its two parameters, various dynamical behaviors are found in the proposed autonomous jerk oscillator including periodic attractor, one-scroll chaotic attractor, and coexistence between chaotic and periodic attractors. The proposed autonomous jerk oscillator has period-doubling route to chaos with the variation of one of its parameters and reverse period-doubling route to chaos with the variation of its other parameter. The proposed autonomous jerk oscillator is modelled on Field Programmable Gate Array (FPGA) and the FPGA chip statistics and phase portraits are derived. The chaotic and coexistence of attractors generated in the proposed autonomous jerk oscillator are confirmed by FPGA implementation of the proposed autonomous jerk oscillator. A good qualitative agreement is illustrated between the numerical and FPGA results. Finally synchronization of unidirectional coupled identical proposed autonomous jerk oscillators is achieved using adaptive sliding mode control method.

THE FEASIBLE DOMAINS AND THEIR BIFURCATIONS IN AN EXTENDED LOGISTIC MODEL WITH AN EXTERNAL INTERFERENCE

2007 ◽  
Vol 17 (03) ◽  
pp. 877-889 ◽  
Author(s):  
EN-GUO GU
Keyword(s):  
Discrete Model ◽  
Logistic Model ◽  
Focal Point ◽  
Basins Of Attraction ◽  
Two Dimensional ◽  
External Interference ◽  
Feasible Set ◽  
Coexistence Of Attractors

This paper is devoted to the study of the properties of basins of attraction and the domains of feasible trajectories (discrete trajectories having an ecological sense) generated by a family of two-dimensional map T related to a discrete model of populations generation. The inverse of T has vanishing denominator giving rise to nonclassical singularities: a nondefinition line, a focal point and a prefocal line. Furthermore, the differences and relations between the feasible set, the feasible domains and the basins of attraction are presented. A phenomena of coexistence of attractors is shown. The structure of a chaotic repellor is interpreted by use of the singularities.

Dynamics of a Piecewise-Linear Oscillator With Limited Power Supply

2009 ◽  
Author(s):  
Silvio L. T. de Souza ◽  
Ibereˆ L. Caldas ◽  
Jose´ M. Balthazar ◽  
Reyolando M. L. R. F. Brasil
Keyword(s):  
Power Supply ◽  
Piecewise Linear ◽  
Basins Of Attraction ◽  
Point Of View ◽  
Restoring Force ◽  
Rich Variety ◽  
Coexistence Of Attractors ◽  
Limited Power ◽  
Limited Power Supply ◽  
Basins Of Attractions

We discuss dynamics of a vibro-impact system consisting of a cart with an piecewise-linear restoring force, which vibrates under driving by a source with limited power supply. From the point of view of dynamical systems, vibro-impact systems exhibit a rich variety of phenomena, particularly chaotic motion. In our analyzes, we use bifurcation diagrams, basins of attractions, identifying several non-linear phenomena, such as chaotic regimes, crises, intermittent mechanisms, and coexistence of attractors with complex basins of attraction.

Fundamental Sources of Economic Complexity

2016 ◽  
Vol 17 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Aleksander Jakimowicz
Keyword(s):  
Deterministic Chaos ◽  
Final State ◽  
Economic Complexity ◽  
Coexistence Of Attractors ◽  
Long Term Effect ◽  
Duopoly Model ◽  
Sensitive Dependence ◽  
Business Cycle Model ◽  
The Business Cycle

AbstractThis article analyses the basic sources and types of economic complexity: chaotic attractors and repellers, complexity catastrophes, coexistence of attractors, sensitive dependence on parameters, final state sensitivity, effects of fractal basin boundaries and chaotic saddles. Four nonlinear classic models have been used for this purpose: virtual duopoly model, model of a centrally planned economy, cobweb model with adaptive expectations and the business cycle model. The issue of economic complexity has not been sufficiently dealt with in the literature. Studies of complexity in economics usually focus on identifying the conditions under which deterministic chaos emerges in models as the main form of complexity, while analyses of other forms of complexity are much less frequent. The article has two objectives: methodological and explicative, which are to shed some new light on the issue. The first objective is to make as comprehensive a catalogue of sources of economic complexity as possible; this is to be achieved by the numerical calculations presented in this article. The issue of accumulation of complexity has been emphasized, which is a type of system dynamics which has its roots in coincidence and overlapping of complexity originating in different sources. The second objective involves an explanation of the role which is played in generating complexity by classic laws of economics. It appears that there is another overarching law, which is independent of the type of system or the level of economic analysis, which states that the long-term effect of conventional economic laws is an inevitable increase in the complexity of markets and economies. Therefore, the sources of complexity discussed in this article are called fundamental ones.

Coexistence of Chaos with Hyperchaos, Period-3 Doubling Bifurcation, and Transient Chaos in the Hyperchaotic Oscillator with Gyrators

2015 ◽  
Vol 25 (04) ◽  
pp. 1550052 ◽  
Author(s):  
J. Kengne
Keyword(s):  
Integrated Circuit ◽  
Nonlinear Dynamical Systems ◽  
Piecewise Linear ◽  
Phase Portraits ◽  
Piecewise Linear Approximation ◽  
Transient Chaos ◽  
Frequency Spectra ◽  
Nonlinear Dynamical ◽  
System Parameters ◽  
Coexistence Of Attractors

In this paper, the dynamics of the paradigmatic hyperchaotic oscillator with gyrators introduced by Tamasevicius and co-workers (referred to as the TCMNL oscillator hereafter) is considered. This well known hyperchaotic oscillator with active RC realization of inductors is suitable for integrated circuit implementation. Unlike previous literature based on piecewise-linear approximation methods, I derive a new (smooth) mathematical model based on the Shockley diode equation to explore the dynamics of the oscillator. Various tools for detecting chaos including bifurcation diagrams, Lyapunov exponents, frequency spectra, phase portraits and Poincaré sections are exploited to establish the connection between the system parameters and various complex dynamic regimes (e.g. hyperchaos, period-3 doubling bifurcation, coexistence of attractors, transient chaos) of the hyperchaotic oscillator. One of the most interesting and striking features of this oscillator discovered/revealed in this work is the coexistence of a hyperchaotic attractor with a chaotic one over a broad range of system parameters. This phenomenon was not reported previously and therefore represents a meaningful contribution to the understanding of the behavior of nonlinear dynamical systems in general. A close agreement is observed between theoretical and experimental analyses.

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