TY - JOUR

T1 - Stable periodic solutions of a spatially homogeneous nonlocal reaction-diffusion equation

AU - Poláčik, Peter

AU - Šošovička, Vladimír

PY - 1996/1/1

Y1 - 1996/1/1

N2 - Nonlocal reaction-diffusion equations of the form ut = uxx + F(u, α(u)), where α(u) = ∫-1 1 u(x) dx, are considered together with Neumann or Dirichlet boundary conditions. One of the main results deals with linearisation at equilibria. It states that, for any given set of complex numbers, one can arrange, choosing the equation properly, that this set is contained in the spectrum of the linearisation. The second main result shows that equations of the above form can undergo a supercritical Hopf bifurcation to an asymptotically stable periodic solution.

AB - Nonlocal reaction-diffusion equations of the form ut = uxx + F(u, α(u)), where α(u) = ∫-1 1 u(x) dx, are considered together with Neumann or Dirichlet boundary conditions. One of the main results deals with linearisation at equilibria. It states that, for any given set of complex numbers, one can arrange, choosing the equation properly, that this set is contained in the spectrum of the linearisation. The second main result shows that equations of the above form can undergo a supercritical Hopf bifurcation to an asymptotically stable periodic solution.

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U2 - 10.1017/S0308210500023118

DO - 10.1017/S0308210500023118

M3 - Article

AN - SCOPUS:21344468661

VL - 126

SP - 867

EP - 884

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

SN - 0308-2105

IS - 4

ER -