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Linearly stable subharmonic orbits in strongly monotone time-periodic dynamical systems


Author: Peter Takáč
Journal: Proc. Amer. Math. Soc. 115 (1992), 691-698
MSC: Primary 34C25; Secondary 34G20, 35K57, 58F22
DOI: https://doi.org/10.1090/S0002-9939-1992-1098406-9
MathSciNet review: 1098406
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Abstract: We construct two simple examples of strongly monotone time-periodic dynamical systems (of period $ \tau > 0$) possessing linearly stable subharmonic orbits of period $ n\tau $ for any integer $ n \geq 2$. The first example is an irreducible cooperative system of four ODE's that models positive feedback. The second example is a one-dimensional reaction-diffusion PDE with periodic boundary conditions. Our construction employs Chebyshev's polynomials.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1098406-9
Keywords: Positive feedback system, reaction-diffusion equation, strongly monotone mapping, period map, linearly stable cycle, Chebyshev's polynomial
Article copyright: © Copyright 1992 American Mathematical Society

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