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 ) possessing linearly stable subharmonic orbits of period for any integer . 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