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Related Concept Videos

Classification of Systems-II01:31

Classification of Systems-II

Continuous-time systems have continuous input and output signals, with time measured continuously. These systems are generally defined by differential or algebraic equations. For instance, in an RC circuit, the relationship between input and output voltage is expressed through a differential equation derived from Ohm's law and the capacitor relation,
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System stability is a fundamental concept in signal processing, often assessed using convolution. For a system to be considered bounded-input bounded-output (BIBO) stable, any bounded input signal must produce a bounded output signal. A bounded input signal is one where the modulus does not exceed a certain constant at any point in time.
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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Optimal periodic orbits of continuous time chaotic systems

Yang1, Hunt, Ott

  • 1Department of Physics, National Cheng Kung University, Tainan 70101, Taiwan.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|November 23, 2000
PubMed
Summary

Optimal orbits on chaotic attractors are typically low-period periodic orbits. For continuous time systems, optimality can occur on steady states, and higher periods may be optimal near attractor crises.

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Area of Science:

  • Dynamical Systems and Chaos Theory
  • Nonlinear Dynamics
  • Statistical Physics

Background:

  • Previous research conjectured optimal orbits on chaotic attractors are typically low-period periodic orbits.
  • Optimality is defined by maximizing a time-averaged performance function of the system state.
  • Optimal orbits are relevant to chaos control, attractor embedding, and synchronized chaotic systems.

Purpose of the Study:

  • Extend previous findings on optimal orbits to continuous time systems (flows).
  • Investigate the role of unstable steady states in optimality for flows.
  • Clarify the conditions under which optimality occurs at higher periods.

Main Methods:

  • Analysis of continuous time dynamical systems.
  • Numerical experiments on chaotic attractors.
  • Investigation of system parameter tuning near attractor crises.

Main Results:

  • Optimality in continuous time systems can occur on unstable steady states, not just periodic orbits.
  • The notion of "typically" low-period optimality is refined.
  • As a system approaches an attractor crisis, optimal orbits may shift to higher periods.

Conclusions:

  • Continuous time systems introduce steady states as potential locations for optimal orbits.
  • The period of optimal orbits is sensitive to system parameters and proximity to attractor crises.
  • Findings advance the understanding of optimal dynamics within chaotic systems.