Journal ArticleDOI
Chaos and hyperchaos in the fractional-order Rössler equations
Chunguang Li,Guanrong Chen +1 more
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In this paper, the authors numerically studied the chaotic behaviors in the fractional-order Rossler equations and found that chaos and hyperchaos exist in such systems with order less than 3.Abstract:
The dynamics of fractional-order systems have attracted increasing attentions in recent years. In this paper, we numerically study the chaotic behaviors in the fractional-order Rossler equations. We found that chaotic behaviors exist in the fractional-order Rossler equation with orders less than 3, and hyperchaos exists in the fractional-order Rossler hyperchaotic equation with order less than 4. The lowest orders we found for chaos and hyperchaos to exist in such systems are 2.4 and 3.8, respectively. Period doubling routes to chaos in the fractional-order Rossler equation are also found.read more
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Fractional Order Systems: Modeling and Control Applications
TL;DR: Fractional Order Systems Fractional order PID Controller Chaotic fractional order systems Field Programmable Gate Array, Microcontroller and Field Pmable Analog Array Implementation Switched Capacitor and Integrated Circuit Design Modeling of Ionic Polymeric Metal Composite as discussed by the authors.
Journal ArticleDOI
Chaos in the fractional order Chen system and its control
Chunguang Li,Guanrong Chen +1 more
TL;DR: In this paper, the authors studied the chaotic behaviors in the fractional order Chen system and found that chaos exists in all the levels of the Chen system with order less than 3.1.
Journal ArticleDOI
Discrete fractional logistic map and its chaos
TL;DR: In this article, a discrete fractional logistic map is proposed in the left Caputo discrete delta sense, which holds discrete memory, and the bifurcation diagrams are given and the chaotic behaviors are numerically illustrated.
Journal ArticleDOI
Nonlinear dynamics and chaos in a fractional-order financial system
TL;DR: A fractional-order financial system is proposed, a generalization of a dynamic financial model recently reported in the literature, that displays many interesting dynamic behaviors, such as fixed points, periodic motions, and chaotic motions.
References
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Journal ArticleDOI
Determining Lyapunov exponents from a time series
TL;DR: In this article, the authors present the first algorithms that allow the estimation of non-negative Lyapunov exponents from an experimental time series, which provide a qualitative and quantitative characterization of dynamical behavior.
Journal ArticleDOI
An equation for continuous chaos
TL;DR: A prototype equation to the Lorenz model of turbulence contains just one (second-order) nonlinearity in one variable as mentioned in this paper, which allows for a "folded" Poincare map (horseshoe map).
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Yet another chaotic attractor
Guanrong Chen,Tetsushi Ueta +1 more
TL;DR: In this paper, the authors reported the finding of a chaotic at tractor in a simple three-dimensional autonomous system, which resembles some familiar features from both the Lorenz and Rossler at tractors.
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Chaos, fractional kinetics, and anomalous transport
TL;DR: In this article, the concept of fractional kinetics is reviewed for systems with Hamiltonian chaos, where the notions of dynamical quasi-traps, Poincare recurrences, Levy flights, exit time distributions, phase space topology, etc.