Optimization problems in population dynamics

Abstract

In this paper we consider initial problems for autonomous differential equations with fixed moments in the form

The following problem has been solved. To determine •the number of implsive moments - n; •the quantities of impulsive subtractings - I₁,I_2:,…I_n; •the impulsive moments - 0<T₁<T₂<…<T_n so that ∘I₀≤I_i≤I,i=1,2…,n where I₀ I are positive constants;a>∘I₁+I₂+…+I_n=I;∘ in the moment T > 0 the solution of considered initial problem will be maximum.It is known the if we have an impulsive analogue to the Verhulst equation, if - the Gompertz model is obtained. The results are applied to the Verhulst and Gompertz models from population dynamics.

Keywords:

• Impulsive differential equations
• Impulsive moments
• Population dynamics
• Impulsive Verhulst and Grompertz models