Asymptotic methods are used to study solutions of a modified logistic equation with a delay containing a large parameter. A result on the existence and stability of a relaxation cycle is given.

This paper investigates the dynamics of the number of specimens in an isolated population living in a heterogeneous environment under the hunting influence. The conclusions regarding optimization of the hunting process are formulated. They are based on the results of the asymptotic analysis of the steady-state operating conditions.

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