Geodesic
Asymptotics of a Steady-State Condition of Finite-Difference Approximation of a Logistic Equation with Delay and Small Diffusion
Modelirovanie i analiz informacionnyh sistem, Tome 21 (2014) no. 1, pp. 94-114

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We study the dynamics of finite-difference approximation on spatial variables of a logistic equation with delay and diffusion. It is assumed that the diffusion coefficient is small and the Malthusian coefficient is large. The question of the existence and asymptotic behavior of attractors was studied with special asymptotic methods. It is shown that there is a rich array of different types of attractors in the phase space: leading centers, spiral waves, etc. The main asymptotic characteristics of all solutions from the corresponding attractors are adduced in this work. Typical graphics of wave fronts motion of different structures are represented in the article.
Keywords: logistic equation, attractor, guiding center, helicon waves, asymptotics, stability. 
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     author = {S. A. Kaschenko and V. E. Frolov},
     title = {Asymptotics of a {Steady-State} {Condition} of {Finite-Difference} {Approximation} of a {Logistic} {Equation} with {Delay} and {Small} {Diffusion}},
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S. A. Kaschenko; V. E. Frolov. Asymptotics of a Steady-State Condition of Finite-Difference Approximation of a Logistic Equation with Delay and Small Diffusion. Modelirovanie i analiz informacionnyh sistem, Tome 21 (2014) no. 1, pp. 94-114. http://geodesic.mathdoc.fr/item/MAIS_2014_21_1_a7/