I-optimal curve for impulsive Lotka-Volterra predator-prey model
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2002-05-01
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Abstract
For the classical Lotka-Volterra predator-prey system, new notion I-optimal curve ξI is introduced. This curve is disposed in the phase space of the system. The curve ξI intersects each trajectory γc of Lotka-Volterra system at least once. The points of ξI possess the following optimal property: if (m, M) ∈ ξI ∩ γc(0), then after a ``jump`` with magnitude I to the origin of coordinates, it hits a trajectory γc(1) and c1 is minimal; i.e., γc(1) is the ``nearest`` to the stable centre. The minimality concerns the rest points of initial trajectory γc(0), from which the ``impulsive jumps`` (subtractings) with magnitude I to (0, 0) are realized. The monotonicity, continuity, and linear asymptotical behaviour of ξI curve are proved. © 2002 Elsevier Science Ltd. All rights reserved.