Geodesic
Dynamics of the logistic delay equation with a large spatially distributed control coefficient
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 5, pp. 766-778

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The local dynamics of the logistic delay equation with a large spatially distributed control coefficient is asymptotically studied. The basic bifurcation scenarios are analyzed depending on the relations between the parameters of the equation. It is shown that the equilibrium states can lose stability even for asymptotically small values of the delay parameter. The corresponding critical cases can have an infinite dimension. Special nonlinear parabolic equations are constructed whose nonlocal dynamics determine the local behavior of solutions to the original boundary value problem. 
@article{ZVMMF_2014_54_5_a5,
     author = {I. S. Kashchenko and S. A. Kashchenko},
     title = {Dynamics of the logistic delay equation with a large spatially distributed control coefficient},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {766--778},
     publisher = {mathdoc},
     volume = {54},
     number = {5},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_5_a5/}
}
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I. S. Kashchenko; S. A. Kashchenko. Dynamics of the logistic delay equation with a large spatially distributed control coefficient. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 54 (2014) no. 5, pp. 766-778. http://geodesic.mathdoc.fr/item/ZVMMF_2014_54_5_a5/