Seminar Abstract yDynamics for the Competitive N-Individual Interactionsz ------------------------------ Speaker: ɓ h ( http://www.ism.ac.jp/~itoh/ ) Affiliation: v ̈擝vn Date and Time: 2002. 6. 6 (Thu), 4:30 - 6:00 p.m. Place: 3F1136 Chair: HR pO ------------------------------ Abstract: Binary interactions may not be sufficient to model all situations of biological interest. At high population densities, three, four or more individuals may interact as for the Boltzmann equation for higher densities. A differential equations model with ternary interactions is analyzed by using non-associative algebra (Itoh (1975, 1981) Itoh and Cohen (1994)), where a certain Lyapunov function increases until the system attains equilibrium. For the corresponding model with only binary interactions, the same Lyapunov function is invariant with respect to time. Thus the term that represents ternary interactions makes a qualitative difference to the model's behavior and justifies, from the mathematical point of view, the study of models with ternary and higher order interactions. A game dynamics will be discussed for the model. References - Itoh, Y.,(1975), An H-Theorem for a System of Competing Species, Proc. Japan Acad. 51, 374-379. - Itoh, Y. (1981). Non-associative algebra and Lotka-Volterra equation with ternary interaction, Nonlinear Anal., 5, 53-56. - Itoh, Y. and Cohen J. E.(1993) Competitive ternary interactions and relative entropy of solutions, J. Phys. A 27, 6383-6393.