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Bifurcation delay in nonlinear systems with time-scaling.

Deepak Rawat1, Suresh Kumarasamy2,3, Awadhesh Prasad1

  • 1Department of Physics and Astrophysics, University of Delhi, Delhi 110007, India.

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Dynamic bifurcations in systems with time-varying parameters cause a delay. This study explains how time-scaling affects this bifurcation delay in ecological and neuron models, revealing a predictable asymptotic relationship.

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Area of Science:

  • Nonlinear Dynamics
  • Theoretical Physics
  • Computational Biology

Background:

  • Dynamical systems with time-dependent parameters exhibit dynamic bifurcations.
  • Dynamic bifurcations result in a phenomenon known as bifurcation delay or postponement.
  • The extent of this delay is influenced by the frequency of parameter variation.

Purpose of the Study:

  • To provide numerical and analytical explanations for the influence of time-scaling on dynamic bifurcation.
  • To investigate how time-scaling affects the bifurcation delay in nonlinear dynamical systems.
  • To explore potential applications of these findings.

Main Methods:

  • Numerical simulations of nonlinear dynamical systems.
  • Analytical derivations to explain observed phenomena.
  • Analysis of two distinct systems: an ecological model and a neuron model.

Main Results:

  • Demonstrated a generic behavior in bifurcation delay across different systems.
  • Showed that bifurcation delay follows an asymptotic expression dependent on time-scaling.
  • Identified the impact of parameter time-dependence on bifurcation phenomena.

Conclusions:

  • Time-scaling is a critical factor influencing bifurcation delay in dynamical systems.
  • The relationship between time-scaling and bifurcation delay can be described by an asymptotic expression.
  • Understanding this phenomenon has implications for modeling complex systems in ecology and neuroscience.