TY - JOUR
T1 - Stable periodic solutions of a spatially homogeneous nonlocal reaction-diffusion equation
AU - Poláčik, Peter
AU - Šošovička, Vladimír
PY - 1996
Y1 - 1996
N2 - Nonlocal reaction-diffusion equations of the form ut = uxx + F(u, α(u)), where α(u) = ∫-11 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) = ∫-11 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
SN - 0308-2105
VL - 126
SP - 867
EP - 884
JO - Royal Society of Edinburgh - Proceedings A
JF - Royal Society of Edinburgh - Proceedings A
IS - 4
ER -