Hidden attractors in dynamical systems

By Dawid Dudkowski, Sajad Jafari, Tomasz Kapitaniak, Nikolay V. Kuznetsov, Gennady A. Leonov, Awadhesh Prasad. 2016

730 citations recorded by the source corpus.

Abstract Complex dynamical systems, ranging from the climate, ecosystems to financial markets and engineering applications typically have many coexisting attractors. This property of the system is called multistability. The final state, i.e., the attractor on which the multistable system evolves strongly depends on the initial conditions. Additionally, such systems are very sensitive towards noise and system parameters so a sudden shift to a contrasting regime may occur. To understand the dynamics of these systems one has to identify all possible attractors and their basins of attraction. Recently, it has been shown that multistability is connected with the occurrence of unpredictable attractors which have been called hidden attractors. The basins of attraction of the hidden attractors do not touch unstable fixed points (if exists) and are located far away from such points. Numerical localization of the hidden attractors is not straightforward since there are no transient processes leading to them from the neighborhoods of unstable fixed points and one has to use the special analytical–numerical procedures. From the viewpoint of applications, the identification of hidden attractors is the major issue. The knowledge about the emergence and properties of hidden attractors can increase the likelihood that the system will remain on the most desirable attractor and reduce the risk of the sudden jump to undesired behavior. We review the most representative examples of hidden attractors, discuss their theoretical properties and experimental observations. We also describe numerical methods which allow identification of the hidden attractors.

Subfields: Computer Networks and Communications, Global and Planetary Change, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/6792ed019113e1dbf3f9b8fcc754d18661b5e1d5

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In Computer Networks and Communications

  1. Nikolay V. Kuznetsov
  2. Gennady A. Leonov
  3. Awadhesh Prasad
  4. Sajad Jafari
  5. Julien Clinton Sprott

In Statistical and Nonlinear Physics

  1. Nikolay V. Kuznetsov
  2. Gennady A. Leonov
  3. Awadhesh Prasad
  4. Sajad Jafari
  5. Julien Clinton Sprott
  6. Vladimir I. Vagaitsev

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