Four-wing hyperchaotic attractor generated from a new 4D system with one equilibrium and its fractional-order form

In this paper, we investigate adaptive switched generalized function projective synchronization between two new different hyperchaotic systems with unknown parameters, which is an extension of the switched modified function projective synchronization scheme. Based on the Lyapunov stability theory, corresponding adaptive controllers with appropriate parameter update laws are constructed to achieve adaptive switched generalized function projective synchronization between two different hyperchaotic systems. A numerical simulation is conducted to illustrate the validity and feasibility of the proposed synchronization scheme.

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“…Lately, Dadras et al [46] reported the following four-wing hyperchaotic system, which has only one unstable equilibrium…”

Section: Description Of the Switched Generalized Function Projective mentioning

confidence: 99%

“…When a = 8, b = 40 and r = 14.9, and with the initial condition [10,1,10,1] T , system (5) is hyperchaotic and its attractor is shown in Figure 2. For more information on the dynamical behaviors of these two systems, please refer to [45,46].…”

Section: Description Of the Switched Generalized Function Projective mentioning

confidence: 99%

Adaptive Switched Generalized Function Projective Synchronization between Two Hyperchaotic Systems with Unknown Parameters

Zhou

Xiong

Cai

2013

Entropy

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“…There has been an increasing amount of literature on hyperchaos [7,8]. Authors have introduced and studied different hyperchaotic systems such as switched hyperchaotic system [9], four-wing hyperchaotic attractor [10], hyperchaotic Chua's circuits [11], and hyperchaotic Lü attractor [12]. It is noted that there are countable numbers of equilibrium points in such reported hyperchaotic systems.…”

Section: Introductionmentioning

confidence: 99%

A No-Equilibrium Hyperchaotic System and Its Fractional-Order Form

Hoàng

Kingni

Pham

2017

Mathematical Problems in Engineering

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No-equilibrium system with chaotic behavior has attracted considerable attention recently because of its hidden attractor. We study a new four-dimensional system without equilibrium in this work. The new no-equilibrium system exhibits hyperchaos and coexisting attractors. Amplitude control feature of the system is also discovered. The commensurate fractional-order version of the proposed system is studied using numerical simulations. By tuning the commensurate fractional-order, the proposed system displays a wide variety of dynamical behaviors ranging from coexistence of quasiperiodic and chaotic attractors and bistable chaotic attractors to point attractor via transient chaos.

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“…Also, having more than one positive Lyapunov exponents is very important and to obtain them should be increased the system dimensions, but this can lead to instability, and thus, it is hard finding a chaotic system. Having more than one positive Lyapunov exponents causes the system to show very complex behaviors and very irregular responses [35]. Today, these systems are called hyper-chaotic systems with complex dynamical behavior.…”

Section: Introductionmentioning

confidence: 99%

“…Having only one equilibrium point in a four-wing attractor almost impossible, but Dadras and Momeni [35] reported four-wing attractor which has only one equilibrium point that is interesting in itself. The research to find various types of multi-wing attractors has been done recently, so that Qi has introduced an eight-wing attractor with nine equilibrium points in 2012 [42].…”

Section: Introductionmentioning

confidence: 99%

Complex dynamics in a 5-D hyper-chaotic attractor with four-wing, one equilibrium and multiple chaotic attractors

Zarei

2015

Nonlinear Dyn

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In this paper, a new five-dimensional autonomous hyper-chaotic attractor with complex dynamics is introduced. Nonlinear behavior of the proposed system is different with most well-known chaotic and hyper-chaotic attractors and exists interesting aspects in this system. There are eight parameters to control with only one equilibrium point, and the new dynamics can generate four-wing hyperchaotic and chaotic attractors for some specific parameters and initial conditions. One remarkable feature of the new system is that it can generate double-wing and four-wing smooth chaotic attractors with special appearance. By using the symmetry properties about the coordinates, initial conditions and bifurcation diagrams, many schemes are presented to indicate multiscroll or multi-wing systems. The phenomenon of multiple attractors is discussed, which means that several attractors created simultaneously from different initial values, and according to this phenomenon, many strange attractors are obtained. Detailed information on the dynamic of the new system is obtained numerically by means of phase portraits, sensitivity to initial conditions, Lyapunov exponents spectrum, bifurcation diagrams and Poincare maps. The stability analysis of the new attractors has been investigated to understand dynamical behaviors nearby equilibrium points.

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Four-wing hyperchaotic attractor generated from a new 4D system with one equilibrium and its fractional-order form

Cited by 81 publications

References 58 publications

Adaptive Switched Generalized Function Projective Synchronization between Two Hyperchaotic Systems with Unknown Parameters

Adaptive Switched Generalized Function Projective Synchronization between Two Hyperchaotic Systems with Unknown Parameters

A No-Equilibrium Hyperchaotic System and Its Fractional-Order Form

Complex dynamics in a 5-D hyper-chaotic attractor with four-wing, one equilibrium and multiple chaotic attractors

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