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Volume 4,     Number 1,     Winter 1996

 

LOCAL-NONLOCAL INTERACTION AND
SPATIAL-TEMPORAL PATTERNS
IN SINGLE SPECIES POPULATION OVER
A PATCHY ENVIRONMENT
NEAL MADRAS, JIANHONG WU AND XINGFU ZOU

Abstract. A system of functional differential equations is proposed to describe the dynamics of a single-species population distributed over a patchy environment. Of major concern is the impact of the interaction between local aggregation and global delayed competition on the dynamics and the spatial-temporal patterns of the considered system. It is shown that spatially heterogeneous steady state solutions can bifurcate from a spatially homogeneous steady state solution if the dispersion rate is large. Moreover, Hopf bifurcation of periodic solutions including phase-locked oscillations and synchronous oscillations can occur when the time delay in the global intraspecies competition reaches a critical value. Examples are provided to exhibit the complexity of the dynamics and the co-existence of phase-locked oscillations and heterogeneous steady state solutions.

 

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