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Global convergence of delayed dynamical systems.

T Chen1

  • 1Inst. of Math., Fudan Univ., Shanghai.

IEEE Transactions on Neural Networks
|February 6, 2008
PubMed
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This study explores the stability of delayed dynamical systems in a critical case. We confirm stability is maintained even when coefficient inequalities become non-strict, particularly for hyperbolic tangent activation functions.

Area of Science:

  • Dynamical Systems
  • Control Theory
  • Nonlinear Analysis

Background:

  • Delayed dynamical systems are crucial in modeling real-world phenomena.
  • Stability analysis typically relies on strict inequalities for system coefficients.
  • The behavior of these systems under non-strict inequalities remains an open question.

Purpose of the Study:

  • To investigate the stability and convergence of delayed dynamical systems in a critical case.
  • To determine if stability is preserved when strict inequalities are relaxed to non-strict inequalities.
  • To provide an affirmative answer for systems with hyperbolic tangent activation functions.

Main Methods:

  • Analysis of delayed dynamical systems.
  • Investigation of coefficient inequalities.

Related Experiment Videos

  • Focus on the critical case where inequalities are non-strict.
  • Application to systems with hyperbolic tangent activation functions.

    • Main Results:

    • Demonstrated that delayed dynamical systems can maintain stability in the critical case.
    • Showed that non-strict inequalities do not necessarily lead to instability.
    • Confirmed affirmative results for systems employing hyperbolic tangent activation functions.

    Conclusions:

    • Stability in delayed dynamical systems can be achieved under non-strict coefficient conditions.
    • The critical case analysis provides valuable insights for system design.
    • Hyperbolic tangent activation functions are robust in these critical stability scenarios.