A.N. Katulev, A.Yu. Kuznetsov
The algorithm of investigation of stability of solutions of nonlinear systems of differential equations is suggested on the basis of analysis of stability of correspondent conjugate Hamiltonian systems without introduction Lyapunov function. The algorithm may be use for study of stability of solutions of different nonlinear differential systems of second and higher orders, for investigation of stability of solutions of gomogenious systems of nonlinear integral Volterra equations of second genus, and also for study of bifurcation set of solutions of nonlinear systems. The worked out approach to decision of wide class of stability problems is development of Erugin–Aizerman approach.