On the geometric structures in evolutionary games on square and triangular lattices
We study a model of a spatial evolutionary game, based on the Prisoner’s dilemma
for two regular arrangements of players, on a square lattice and on a triangular lattice.
We analyze steady state distributions of players which evolve from irregular, random initial
configurations. We find significant differences between the square and triangular lattice, and we
characterize the geometric structures which emerge on the triangular lattice.
We investigate geometrical aspects of a spatial evolutionary game. The game is based on the Prisoner's dilemma. We analyze the geometrical structure of the space distribution of cooperators and defectors in the steady-state regime of evolution. We develop algorithm for the identification of the interfaces between clusters of cooperators and defectors, and measure fractal properties of the interfaces.
The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.
Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.