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A conservation law and stability, recovering phenomena and characteristicpatterns of a nonlinear dynamical system have been studied and applied tobiological and ecological systems. In our previous study, we proposed a systemof symmetric 2n-dimensional conserved nonlinear differential equations withexternal perturbations. In this paper, competitive systems described by2-dimensional nonlinear dynamical (ND) model with external perturbations areapplied to population cycles and recovering phenomena of systems from microbesto mammals. The famous 10-year cycle of population density of Canadian lynx andsnowshoe hare is numerically analyzed. We find that a nonlinear dynamicalsystem with a conservation law is stable and generates a characteristic rhythm(cycle) of population density, which we call the {\it standard rhythm} of anonlinear dynamical system. The stability and restoration phenomena arestrongly related to a conservation law and balance of a system. The {\itstandard rhythm} of population density is a manifestation of the survival ofthe fittest to the balance of a nonlinear dynamical system.

Stability and Restoration phenomena in Competitive Systems