I-optimal curve for impulsive Lotka—Volterra predator-prey model

✍ Scribed by J. Angelova; A. Dishliev; S. Nenov

• Publisher: Elsevier Science
• Year: 2002
• Tongue: English
• Weight: 961 KB
• Volume: 43
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(02)00092-5

✦ Synopsis

For

the classical Lotka-Volterra predator-prey system, new notion I-optimal curve ~1 is introduced. This curve is disposed in the phase space of the system. The curve <I intersects each trajectory yc of Lotka-Volterra system at least once. The points of (1 possess the following optimal property: if (m, hl) E <I n yco, then after a "jump" with magnitude I to the origin of coordinates. it hits a trajectory yci and ci is minimal; i.e., yc, is the "nearest" to the stable centre. The minimality concerns the rest points of initial trajectory ycO, from which the "impulsive jumps" (subtractings) with magnitude I to (0,O) are realized. The monotonicity, continuityl a.nd linear asymptotical behaviour of <I curve are proved.