ИСТИНА

In this work using the variational method the stability of the equilibrium states of a nonlinear dynamic system was studied [1]: where − fixed parameters. This system is, of course, nonlinear and more perspective from the point of view of its analysis than the well-known mathematical model “the brusselator” considered in [2]. The variational method [3] is particularly effective when the Lyapunov’s method does not give the desired result or creates insurmountable difficulties or causes inaccuracies in its application. The proposed method is simple to implement and allows you to serve as an incentive for further research in this direction. The proposed nonlinear dynamic system has five stationary points (equilibrium positions): , and , where , . For the zero (trivial) equilibrium position just prove that the perturbed solution is stable only if . For the equilibrium position it is proved that the necessary stability conditions for the perturbed solution are valid if the inequality . For the equilibrium position it is established that the necessary stability conditions for the perturbed solution are valid if it is satisfied that .