BIFURCATION AND STABILITY OF STEADY SOLUTIONS OF EVOLUTION EQUATIONS

BIFURCATION AND STABILITY OF STEADY SOLUTIONS OF EVOLUTION EQUATIONS

ABSTRACT

We considered the evolutional problems in two-dimensional autonomous system. We showed that the bifurcating steady solutions are obtained from the points of intersection of the two conic sections and we used the implicit function theorem to justify their existence, and also we applied the Lyapunov theorem to establish their stability.