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Analysis of thermostat models

Published online by Cambridge University Press:  01 October 1997

B. CAHLON ,
D. SCHMIDT ,
M. SHILLOR  and
X. ZOU
B. CAHLON
Affiliation:
Department of Mathematical Sciences, Oakland University, Rochester, MI 48309, USA
D. SCHMIDT
Affiliation:
Department of Mathematical Sciences, Oakland University, Rochester, MI 48309, USA
M. SHILLOR
Affiliation:
Department of Mathematical Sciences, Oakland University, Rochester, MI 48309, USA
X. ZOU
Affiliation:
Department of Mathematical Sciences, Oakland University, Rochester, MI 48309, USA
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Abstract

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We present two new models describing the dynamic behavior of an automotive thermostat, involving delay-differential equations with hysteresis. Existence, uniqueness, and regularity of the solutions for both models are obtained by a continuation argument. We establish sufficient conditions for the models to exhibit intrinsic oscillations. We also present an algorithm for numerical approximations of the solutions and give some representative numerical simulations. These reveal a rather interesting dynamical behavior of the solutions.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 8 , Issue 5 , October 1997 , pp. 437 - 455
Copyright
© 1997 Cambridge University Press