Controlling Dynamics of Hidden Attractors

Sharma, Pradeep; Shrimali, Manish Dev; Prasad, Awadhesh; Kuznetsov, Nikolay V.; Леонов, Г. А.

doi:10.1142/s0218127415500613

Cited by 121 publications

(39 citation statements)

References 25 publications

(23 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…It is worth noting that systems with stable equilibria are systems with 'hidden attractors' [26][27][28][29]. Hidden attractors have received considerable attention recently because of their roles in theoretical and practical problems [30][31][32][33][34][35][36][37][38]. Different definitions and main properties of fractional calculus have been reported in the literature [47][48][49][50].…”

Section: Introductionmentioning

confidence: 99%

A fractional-order form of a system with stable equilibria and its synchronization

et al. 2018

View full text Add to dashboard Cite

There has been an increasing interest in studying fractional-order chaotic systems and their synchronization. In this paper, the fractional-order form of a system with stable equilibrium is introduced. It is interesting that such a three-dimensional fractional system can exhibit chaotic attractors. Full-state hybrid projective synchronization scheme and inverse full-state hybrid projective synchronization scheme have been designed to synchronize the three-dimensional fractional system with different four-dimensional fractional systems. Numerical examples have verified the proposed synchronization schemes.

show abstract

Section: Introductionmentioning

confidence: 99%

A fractional-order form of a system with stable equilibria and its synchronization

et al. 2018

View full text Add to dashboard Cite

show abstract

“…The rst one is hidden attractor. An attractor is called hidden if its basin of attraction does not intersect with a small neighborhood of any equilibrium point [15][16][17][18]. The second one is self-excited attractor.…”

Section: Introductionmentioning

confidence: 99%

A new three-dimensional chaotic flow with one stable equilibrium: dynamical properties and complexity analysis

Khalaf¹,

Kapitaniak²,

Rajagopal³

et al. 2018

Open Physics

View full text Add to dashboard Cite

This paper proposes a new three-dimensional chaotic ow with one stable equilibrium. Dynamical properties of this system are investigated. The system has a chaotic attractor coexisting with a stable equilibrium. Thus the chaotic attractor is hidden. Basin of attractions shows the tangle of di erent attractors. Also, some complexity measures of the system such as Lyapunov exponent and entropy will are analyzed. We show that the Kolmogorov-Sinai Entropy shows more accurate results in comparison with Shanon Entropy.

show abstract

“…In the past few years, a new type of attractor, defined as hidden attractor, has been found in large numbers of nonlinear dynamical systems [19][20][21][22][23][24][25]. Different from self-excited attractor, hidden attractor, whose attraction basin does not intersect with small neighborhoods of the equilibria of the system [19][20][21], is sensitive to the initial conditions and special analytical-numerical procedure should be adopted to locate its attractive basin [20].…”

Section: Introductionmentioning

confidence: 99%

Novel 3-Scroll Chua’s Attractor with One Saddle-Focus and Two Stable Node-Foci

Chu

Zhu

Qian

et al. 2018

Mathematical Problems in Engineering

View full text Add to dashboard Cite

With new three-segment piecewise-linearity in the classic Chua's system, two new types of 2-scroll and 3-scroll Chua's attractors are found in this paper. By changing the outer segment slope of the three-segment piecewise-linearity as positive, the new 2-scroll Chua's attractor has emerged from one zero index-1 saddle-focus and two symmetric stable nonzero node-foci. In particular, by newly introducing a piecewise-linear control function, an improved Chua's system only with one zero index-2 saddle-focus and two stable nonzero node-foci is constructed, from which a 3-scroll Chua's attractor is converged. Some remarks for Chua's nonlinearities and the generating chaotic attractors are discussed, and the stabilities at the three equilibrium points are then analyzed, upon which the emerging mechanisms of the novel 2-scroll and 3-scroll Chua's attractors are explored in depth. Furthermore, an analog electronic circuit built with operational amplifier and analog multiplier is designed and hardware circuit experiments are measured to verify the numerical simulations. These novel 2-scroll and 3-scroll Chua's attractors reported in this paper are completely different from the classic Chua's attractors, which will enrich the dynamics of the classic Chua's system.

show abstract

Controlling Dynamics of Hidden Attractors

Cited by 121 publications

References 25 publications

A fractional-order form of a system with stable equilibria and its synchronization

A fractional-order form of a system with stable equilibria and its synchronization

A new three-dimensional chaotic flow with one stable equilibrium: dynamical properties and complexity analysis

Novel 3-Scroll Chua’s Attractor with One Saddle-Focus and Two Stable Node-Foci

Contact Info

Product

Resources

About