Complex dynamics, hidden attractors and continuous approximation of a fractional-order hyperchaotic PWC system

Danca, Marius‐F.; Fečkan, Michal; Kuznetsov, Nikolay V.; Chen, Guanrong

doi:10.1007/s11071-017-4029-5

Cited by 38 publications

(30 citation statements)

References 37 publications

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“…On other words, there can only be asymptotically bounded or unbounded periodic solutions in fractional‐order systems. For more details, see other studies() and references therein.…”

Section: Numerical Simulationmentioning

confidence: 99%

“…These orbits are referred to as, if exist, bounded S‐asymptotically N‐periodic orbits. In literature, these apparently periodic motions are called numerically periodic oscillations . The exploration results of these orbits in space of parameters are better visualized via parameters basin of attractions graphs or two‐dimensional (2‐D) bifurcation diagrams.…”

Section: Numerical Simulationmentioning

confidence: 99%

“…In literature, these apparently periodic motions are called numerically periodic oscillations. 50 The exploration results of these orbits in space of parameters are better visualized via parameters basin of attractions graphs or two-dimensional (2-D) bifurcation diagrams. In these plots, each colored region represents a domain in parameters space corresponding to a specific N of bounded S-asymptotically N-periodic solution.…”

Section: Numerical Simulationmentioning

confidence: 99%

See 2 more Smart Citations

Complex dynamics of a discrete fractional‐order Leslie‐Gower predator‐prey model

Singh

Elsadany

Elsonbaty

2019

Math Methods in App Sciences

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A proposed discretized form of fractional‐order prey‐predator model is investigated. A sufficient condition for the solution of the discrete system to exist and to be unique is determined. Jury stability test is applied for studying stability of equilibrium points of the discretized system. Then, the effects of varying fractional order and other parameters of the systems on its dynamics are examined. The system undergoes Neimark‐Sacker and flip bifurcation under certain conditions. We observe that the model exhibits chaotic dynamics following stable states as the memory parameter α decreases and step size h increases. Theoretical results illustrate the rich dynamics and complexity of the model. Numerical simulation validates theoretical results and demonstrates the presence of rich dynamical behaviors include S‐asymptotically bounded periodic orbits, quasi‐periodicity, and chaos. The system exhibits a wide range of dynamical behaviors for fractional‐order α key parameter.

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“…On other words, there can only be asymptotically bounded or unbounded periodic solutions in fractional‐order systems. For more details, see other studies() and references therein.…”

Section: Numerical Simulationmentioning

confidence: 99%

Section: Numerical Simulationmentioning

confidence: 99%

Section: Numerical Simulationmentioning

confidence: 99%

See 1 more Smart Citation

Complex dynamics of a discrete fractional‐order Leslie‐Gower predator‐prey model

Singh

Elsadany

Elsonbaty

2019

Math Methods in App Sciences

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“…Similarly this happens with discrete difference equations of FO [40]. Therefore, these orbits are called "numerically stable periodic" (NSP), in the sense that the trajectory, from numerical point of view, can be an extremely near periodic trajectory [41]. ii) Even the bifurcation scenario versus µ (Fig.…”

Section: Remarkmentioning

confidence: 97%

Chaos control in the fractional order logistic map via impulses

2019

Self Cite

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In this paper the chaos control in the discrete logistic map of fractional order is obtained with an impulsive control algorithm. The underlying discrete initial value problem of fractional order is considered in terms of Caputo delta fractional difference. Every ∆ steps, the state variable is instantly modified with the same impulse value, chosen from a bifurcation diagram versus impulse. It is shown that the solution of the impulsive control is bounded. The numerical results are verified via time series, histograms, and the 0-1 test. Several examples are considered.keyword Caputo delta fractional difference; Impulsive chaos control; Discrete logistic map of fractional order; Lyapunov exponent of discrete maps of fractional order; 0-1 test Marius-F. Danca

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“…Another fractional-order chaotic systems were described in other works. [37][38][39] Khalil et al 40 proposed an interesting definition of derivative, this novel operator called conformable fractional derivative generalizes the classical concept of derivative. This derivative is well behaved and obeys the Leibniz rule and chain rule.…”

Section: Introductionmentioning

confidence: 99%

Fractional conformable attractors with low fractality

Morales‐Delgado

Gómez‐Aguilar

Escobar-Jiménez

2018

Math Methods in App Sciences

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In this paper, we considered a fractional conformable derivative of Liouville-Caputo type of fractional-order = n − , which contains a small perturbation and positive integer n values between [0;1] to obtain the solutions of three different fractional conformable attractors (Chen's attractor, Genesio-Tesi's attractor, and Liu's attractor). The fractional conformable Adomian decomposition method is applied to obtain an expansion of the fractional conformable derivative in = n − . The solutions of the fractional chaotic systems are calculated in the form of convergent series. We investigate the dynamics of these attractors by numerical simulations for different fractional orders values and parameter . KEYWORDSadomian decomposition method, chaos, fractional calculus, fractional conformable derivative, low-fractality 6378

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Complex dynamics, hidden attractors and continuous approximation of a fractional-order hyperchaotic PWC system

Cited by 38 publications

References 37 publications

Complex dynamics of a discrete fractional‐order Leslie‐Gower predator‐prey model

Complex dynamics of a discrete fractional‐order Leslie‐Gower predator‐prey model

Chaos control in the fractional order logistic map via impulses

Fractional conformable attractors with low fractality

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