The Relationship Between Chaotic Maps and Some Chaotic Systems with Hidden Attractors

Jafari, Sajad; Pham, Viet–Thanh; Golpayegani, Seyed Mohammad Reza Hashemi; Moghtadaei, Motahareh; Kingni, Sifeu Takougang

doi:10.1142/s0218127416502114

Cited by 79 publications

(35 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The maps with hidden dynamics could be similarly defined. Some hidden attractors in one-dimensional maps were obtained by extending the Logistic map [11], and a class of two-dimensional quadratic maps with hidden dynamics was studied in [13].…”

Section: Xu Zhang and Guanrong Chenmentioning

confidence: 99%

Polynomial maps with hidden complex dynamics

Zhang

Chen²

2019

Discrete &Amp; Continuous Dynamical Systems - B

View full text Add to dashboard Cite

The dynamics of a class of one-dimensional polynomial maps are studied, and interesting dynamics are observed under certain conditions: the existence of periodic points with even periods except for one fixed point; the coexistence of two attractors, an attracting fixed point and a hidden attractor; the existence of a double period-doubling bifurcation, which is different from the classical period-doubling bifurcation of the Logistic map; the existence of Li-Yorke chaos. Furthermore, based on this one-dimensional map, the corresponding generalized Hénon map is investigated, and some interesting dynamics are found for certain parameter values: the coexistence of an attracting fixed point and a hidden attractor; the existence of Smale horseshoe for a subshift of finite type and also Li-Yorke chaos.

show abstract

Section: Xu Zhang and Guanrong Chenmentioning

confidence: 99%

Polynomial maps with hidden complex dynamics

Zhang

Chen²

2019

Discrete &Amp; Continuous Dynamical Systems - B

View full text Add to dashboard Cite

show abstract

“…The classification of attractors as being hidden or self-excited was introduced in connection with the discovery of the first hidden Chua attractor [Kuznetsov et al, 2010;Bragin et al, 2011;Leonov et al, 2012;Kiseleva et al, 2017;Stankevich et al, 2017] and has captured much attention of scientists from around the world (see, e.g. [Burkin & Khien, 2014;Li & Sprott, 2014;Pham et al, 2014;Chen et al, 2015;Kuznetsov et al, 2015;Saha et al, 2015;Semenov et al, 2015;Sharma et al, 2015;Zhusubaliyev et al, 2015;Wi et al, 2015;Jafari et al, 2016;Menacer et al, 2016;Ojoniyi & Njah, 2016;Pham et al, 2016;Rocha & Medrano, 2016;Wei et al, 2016;Zelinka, 2016;Borah & Roy, 2017;Brzeski et al, 2017;Feng & Pan, 2017;Jiang , 2016;Kuznetsov et al, 2017;Ma et al, 2017;Messias & Reinol, 2017;Singh & Roy, 2017;Volos et al, 2017;Wei et al, 2017;Zhang et al, 2017]).…”

Section: Introductionmentioning

confidence: 99%

Graphical Structure of Attraction Basins of Hidden Chaotic Attractors: The Rabinovich–Fabrikant System

Danca

Bourke

Kuznetsov

2019

Int. J. Bifurcation Chaos

View full text Add to dashboard Cite

For systems with hidden attractors and unstable equilibria, the property that hidden attractors are not connected with unstable equilibria is now accepted as one of their main characteristics. To the best of our knowledge this property has not been explored using realtime interactive three-dimensions graphics. Aided by advanced computer graphic analysis, in this paper, we explore this characteristic of a particular nonlinear system with very rich and unusual dynamics, the Rabinovich-Fabrikant system. It is shown that there exists a neighborhood of one of the unstable equilibria within which the initial conditions do not lead to the considered hidden chaotic attractor, but to one of the stable equilibria or are divergent. The trajectories starting from any neighborhood of the other unstable equlibria are attracted either by the stable equilibria, or are divergent.

show abstract

“…The classification of attractors as being hidden or self-excited was introduced by G. Leonov and N. Kuznetsov in connection with the discovery of the first hidden Chua attractor [Leonov & Kuznetsov, 2009;Kuznetsov et al, 2010;Bragin et al, 2011;Leonov et al, 2012;Kuznetsov et al, 2013b;Leonov & Kuznetsov, 2013;Leonov et al, 2015a] and has captured attention of scientists from around the world (see, e.g. [Burkin & Khien, 2014;Li & Sprott, 2014;Chen, 2015;Saha et al, 2015;Feng & Pan, 2017;Zhusubaliyev et al, 2015;Danca, 2016;Kuznetsov et al, 2015;Chen et al, 2015a;Pham et al, 2014;Ojoniyi & Njah, 2016;Rocha & Medrano-T, 2016;Borah & Roy, 2017;Danca et al, 2017;Wei et al, 2016;Pham et al, 2016;Jafari et al, 2016;Dudkowski et al, 2016;Singh & Roy, 2017;Messias & Reinol, 2017;Brzeski et al, 2017;Wei et al, 2017;Chaudhuri & Prasad, 2014;Jiang et al, 2016;Volos et al, 2017]).…”

Section: Introductionmentioning

confidence: 99%

Scenario of the Birth of Hidden Attractors in the Chua Circuit

Stankevich

Kuznetsov

Леонов

et al. 2017

Int. J. Bifurcation Chaos

View full text Add to dashboard Cite

Recently it was shown that in the dynamical model of Chua circuit both the classical selfexcited and hidden chaotic attractors can be found. In this paper the dynamics of the Chua circuit is revisited. The scenario of the chaotic dynamics development and the birth of selfexcited and hidden attractors is studied. It is shown a pitchfork bifurcation in which a pair of symmetric attractors coexists and merges into one symmetric attractor through an attractormerging bifurcation and a splitting of a single attractor into two attractors. The scenario relating the subcritical Hopf bifurcation near equilibrium points and the birth of hidden attractors is discussed.Comment: 20 pages, 11 figure

show abstract

The Relationship Between Chaotic Maps and Some Chaotic Systems with Hidden Attractors

Cited by 79 publications

References 39 publications

Polynomial maps with hidden complex dynamics

Polynomial maps with hidden complex dynamics

Graphical Structure of Attraction Basins of Hidden Chaotic Attractors: The Rabinovich–Fabrikant System

Scenario of the Birth of Hidden Attractors in the Chua Circuit

Contact Info

Product

Resources

About