Hidden attractors in fundamental problems and engineering models

Abstract

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.

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Cited by in corpus (26)

• Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system
• Scenario of the Birth of Hidden Attractors in the Chua Circuit
• The Lyapunov dimension and its estimation via the Leonov method
• The Lyapunov dimension formula for the global attractor of the Lorenz system
• Hidden chaotic attractors in fractional-order systems
• Graphical structure of attraction basins of hidden attractors: the Rabinovich-Fabrikant system
• Hidden and self-exited attractors in a heterogeneous Cournot oligopoly model
• Approximating hidden chaotic attractors via parameter switching
• Hopfield Neuronal Network of Fractional Order: A note on its numerical integration
• Dynamics of the Zeraoulia-Sprott map revisited
• Coexisting Hidden and self-excited attractors in an economic system of integer or fractional order
• Numerical analysis of dynamical systems: unstable periodic orbits, hidden transient chaotic sets, hidden attractors, and finite-time Lyapunov dimension
• Dynamics of the Shapovalov mid-size firm model
• The Lyapunov dimension and its computation for self-excited and hidden attractors in the Glukhovsky-Dolzhansky fluid convection model
• Hidden and self-excited attractors in electromechanical systems with and without equilibria
• Theory of differential inclusions and its application in mechanics
• A short survey on Lyapunov dimension for finite dimensional dynamical systems in Euclidean space
• Unusual dynamics and hidden attractors of the Rabinovich-Fabrikant system
• Optical Costas loop: pull-in range estimation and hidden oscillations
• A note on finite-time Lyapunov dimension of the Rossler attractor
• The Lyapunov dimension, convergency and entropy for a dynamical model of Chua memristor circuit
• Analytical and numerical study of the hidden boundary of practical stability: complex versus real Lorenz systems
• A lower-bound estimate of the Lyapunov dimension for the global attractor of the Lorenz system
• Transient hidden chaotic attractors in a Hopfield neural system
• Nonlinear analysis of PLL by the harmonic balance method
• Hidden and self-excited attractors in Chua circuit: SPICE simulation and synchronization