Half-soliton interaction of population taxis waves in predator-prey systems with pursuit and evasion

M. A. Tsyganov, V. N. Biktashev

Submitted to PRE: 2004/03/14. Accepted: 2004/06/27. Reference: Phys. Rev. E, 70(2):031901, 2004

In this paper, we use numerical simulations to demonstrate a new type of interaction of waves in a mathematical model of "prey-predator" system with taxis, a ``half-soliton'' interaction, when of two colliding waves, one annihilates and the other continues to propagate. We show that this effect depends on the ``ages'', or, equivalently, ``widths' of the colliding waves. In two spatial dimensions we demonstrate the type of interaction, i.e. annihilation, quasi-soliton or half-soliton, depends not only on curvature and width of the colliding waves, but also on the angle of the collision. When conditions of collision are varying in such a way that only a part of a wave survive the collision, then ``taxitons'', compact pieces of solitary waves, may form, which can exist for a significant time.