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Observing a codimension-two heteroclinic bifurcation.

Ryuji Tokunaga1, Yasushi Abe, Takashi Matsumoto

  • 1Institute of Information Science and Electronics, Tsukuba University, Tsukuba Science City 305, JapanDepartment of Electrical Engineering, Waseda University, Tokyo 169, JapanDepartment of Electrical Engineering, Waseda University, Tokyo 169, Japan.

Chaos (Woodbury, N.Y.)
|January 1, 1993
PubMed
Summary
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Researchers experimentally observed and simulated complex behaviors in an electrical circuit. They precisely mapped bifurcation sets, confirming theoretical models of nonlinear dynamics.

Area of Science:

  • Nonlinear Dynamics and Chaos Theory
  • Electrical Engineering and Circuit Analysis

Background:

  • Autonomous third-order electrical circuits can exhibit complex dynamical behaviors.
  • Understanding bifurcations is crucial for predicting circuit behavior and designing stable systems.

Purpose of the Study:

  • To experimentally observe and numerically confirm codimension-two heteroclinic bifurcations.
  • To investigate the interplay of bifurcation parameters in a specific electrical circuit.

Main Methods:

  • Laboratory experiments using programmable resistors to adjust bifurcation parameters.
  • Measurement of codimension-one bifurcation sets in a two-parameter space.
  • Computer simulations and derivation of exact bifurcation equations from piecewise-linear circuit dynamics.

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Main Results:

  • Experimental observation of codimension-two heteroclinic bifurcations.
  • Accurate measurement of multiple codimension-one bifurcation sets.
  • Numerical confirmation of experimental findings through derived bifurcation equations.

Conclusions:

  • The study successfully demonstrates experimental observation of codimension-two heteroclinic bifurcations.
  • The results validate the use of piecewise-linear circuit dynamics for predicting complex bifurcations.
  • This work provides a foundation for further research into nonlinear phenomena in electrical circuits.