Nonlinear dynamics equations and chaos

F. Soltani, G. Drzewiecki

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Nonlinear dynamics and chaotic systems have been of great interest to many scientists and engineers over the past two decades. Many nonlinear systems are a result of mathematical models of physical and biological systems that possess inherent nonlinear properties. In this paper, we focus our attention on a second-degree nonlinear differential equation with a sinusoidal forcing function and constant coefficients; such equations, which are commonly employed for mathematical modeling of biological systems usually possess inherent nonlinear properties. We show that the second-degree nonlinear differential equation system could be aperiodic and therefore the long-term behavior is not predictable. However, in the case of the increased frequency of the sinusoidal input, the system shows somewhat periodic, convergent behavior. The simulations demonstrate how small, seemingly insignificant changes to the parameters (e.g., initial conditions) can dramatically alter the system response.

Original languageEnglish (US)
Title of host publicationProceedings of the IEEE 29th Annual Northeast Bioengineering Conference
EditorsStanley Reisman, Richard Foulds, Bruno Mantilla
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages120-121
Number of pages2
ISBN (Electronic)0780377672
DOIs
StatePublished - 2003
Event29th IEEE Annual Northeast Bioengineering Conference, NEBC 2003 - Newark, United States
Duration: Mar 22 2003Mar 23 2003

Publication series

NameProceedings of the IEEE Annual Northeast Bioengineering Conference, NEBEC
Volume2003-January

Other

Other29th IEEE Annual Northeast Bioengineering Conference, NEBC 2003
Country/TerritoryUnited States
CityNewark
Period3/22/033/23/03

ASJC Scopus subject areas

  • Bioengineering

Keywords

  • Biological systems
  • Biomedical engineering
  • Chaos
  • Differential equations
  • Frequency
  • Hemodynamics
  • Laboratories
  • Mathematical model
  • Nonlinear dynamical systems
  • Nonlinear equations

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