Numerical and experimental studies of attractors in memristor-based Chua’s oscillator with a line of equilibria. Noise-induced effects

Int. J. Bifurcation Chaos

Леонов

et al. 2017

Section: A Attractors Of Dynamical Systemsmentioning

confidence: 99%

Hidden Attractors on One Path: Glukhovsky–Dolzhansky, Lorenz, and Rabinovich Systems

Chen

Int. J. Bifurcation Chaos

Леонов

et al. 2017

“…in [Kuznetsov & Leonov, 2014;Kuznetsov et al, 2016Kuznetsov et al, , 2017bKiseleva et al, 2017]. Also some recent results on various modifications of Chua circuit can be found in [Rocha & Medrano-T, 2015;Bao et al, 2015b;Semenov et al, 2015;Gribov et al, 2016;Kengne, 2017;Zhao et al, 2017;Chen et al, 2017b;Corinto & Forti, 2017].…”

Section: Introductionmentioning

confidence: 93%

Scenario of the Birth of Hidden Attractors in the Chua Circuit

Stankevich

Int. J. Bifurcation Chaos

Леонов

et al. 2017

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

“…See also The European Physical Journal Special Topics: Multistability: Uncovering Hidden Attractors, 2015 (see [113][114][115][116][117][118][119][120][121][122][123][124]).…”

Section: Self-excited and Hidden Attractorsmentioning

confidence: 99%

Hidden Attractors in Fundamental Problems and Engineering Models: A Short Survey

Lecture Notes in Electrical Engineering

2016

Recently a concept of self-excited and hidden attractors was suggested: an attractor is called a self-excited attractor if its basin of attraction overlaps with neighborhood of an equilibrium, otherwise it is called a hidden attractor. For example, hidden attractors are attractors in systems with no equilibria or with only one stable equilibrium (a special case of multistability and coexistence of attractors). While coexisting self-excited attractors can be found using the standard computational procedure, there is no standard way of predicting the existence or coexistence of hidden attractors in a system. In this plenary survey lecture the concept of self-excited and hidden attractors is discussed, and various corresponding examples of self-excited and hidden attractors are considered. The material is mostly based on surveys [1-4].1 Analytical-numerical study of oscillations An oscillation dynamical system can generally be easily numerically localized if the initial data from its open neighborhood in the phase space (with the exception of a minor set of points) lead to a long-term behavior that approaches the oscillation. Such an oscillation (or a set of oscillations) is called an attractor, and its attracting set is called the basin of attraction (i.e., a set of initial data for which the trajectories tend to the attractor).When the theories of dynamical systems, oscillations, and chaos were first developed researchers mainly focused on analyzing equilibria stability, which can be easily done numerically or analytically, and on the birth of periodic or chaotic attractors from unstable equilibria. The structures of many physical dynamical International Conference on Advanced Engineering -Theory and Applications, 2015 (Ho Chi Minh City, Vietnam), http://icaeta.org/, plenary lecture arXiv:1510.04803v1 [nlin.CD] 16 Oct 2015 chaotic attractor in the Lorenz system with other parameters may be self-excited with respect to zero unstable equilibrium only, and the possible existence in the Lorenz system of a hidden chaotic attractor is an open problem.