Premium
Chaotic Behavior in Slowly Varying Systems of Nonlinear Differential Equations
Author(s) -
Keener James P.
Publication year - 1982
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm198267125
Subject(s) - homoclinic orbit , aperiodic graph , chaotic , nonlinear system , mathematics , differential equation , mathematical analysis , flow (mathematics) , differential (mechanical device) , statistical physics , physics , bifurcation , geometry , computer science , thermodynamics , quantum mechanics , combinatorics , artificial intelligence
A technique is developed to find parameter regions of chaotic behavior in certain systems of nonlinear differential equations with slowly varying periodic coefficients. The technique combines previous results on how to find branches of periodic solutions which terminate with a homoclinic orbit and results on how to find chaotic trajectories in the neighborhood of homoclinic trajectories of the autonomous system. The technique is applied to the continuous stirred tank reaction A → B , for which it is shown that a slowly varying periodic flow rate can yield aperiodic temperature fluctuations.