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

Takáč, Peter

doi:10.1090/S0002-9939-1992-1098406-9

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

Proc. Amer. Math. Soc. 115 (1992), 691-698

DOI: https://doi.org/10.1090/S0002-9939-1992-1098406-9

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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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