In this paper, the analytical methods for approximate solutions of periodic motions to chaos in nonlinear dynamical systems are reviewed. Briefly discussed are the traditional analytical methods including the Lagrange stand form, perturbation methods, and method of averaging. A brief literature survey of approximate methods in application is completed, and the weakness of current existing appro...

A convenient form of kinetic equation is derived for pair annihilation of heavy stable particles relevant to the dark matter problem in cosmology. The kinetic equation thus derived extends the on-shell Boltzmann equation in a most straightforward way, including the off-shell effect. A detailed balance equation for the equilibrium abundance is further analyzed. Perturbative analysis of this equa...

The dynamics of networks on Heider's balance theory moves toward reducing the tension by constantly reevaluating interactions to achieve a state balance. Conflict interest, however, is inherent in most complex systems; frequently, there are multiple ideals or states balance, and moving towards one could work against another. In this paper, introducing competitive theory, we study evolution pres...