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A New Two-Dimensional Map with Hidden Attractors.

Chuanfu Wang1, Qun Ding1

  • 1Electronic Engineering College, Heilongjiang University, Harbin 150080, China.

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Summary
This summary is machine-generated.

This study explores hidden dynamics in a new discrete-time map, inspired by Arnold's cat map. It details the map's fixed points and their stability, contributing to understanding hidden attractors in discrete systems.

Keywords:
fixed pointhidden attractorsstability

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Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Discrete-Time Systems

Background:

  • Hidden attractors are primarily studied in continuous-time systems.
  • Few investigations exist for hidden attractors in discrete-time dynamic systems.
  • Classical chaotic attractors (e.g., Logistic map, Arnold's cat map) originate from unstable fixed points.

Purpose of the Study:

  • To investigate the hidden dynamics of a novel two-dimensional discrete-time map.
  • To analyze the existence and stability of fixed points in this new map.
  • To extend the understanding of hidden attractors to discrete dynamical systems.

Main Methods:

  • Development of a new two-dimensional discrete-time map inspired by Arnold's cat map.
  • Analytical investigation of fixed points.
  • Analysis of fixed point stability.

Main Results:

  • The paper details the fixed points of the new map.
  • The stability of these fixed points is thoroughly analyzed.
  • The study characterizes the hidden dynamics exhibited by the map.

Conclusions:

  • The novel discrete-time map exhibits hidden dynamics.
  • Understanding fixed point stability is crucial for characterizing hidden attractors in discrete systems.
  • This research contributes to the limited body of work on hidden attractors in discrete dynamical systems.