Steady State Bifurcation For A Class Of 2D Dynamical Systems

Consider the equation f ( x,λ)= λx-Ax+g(x,λ)=0, we know that we've had some better conclusion about the bifurcation in the neighborhood of point ( 0,λ₀)when the algebraic multiplicity of eigenvalue λ₀ of A is odd 。But,when the algebraic multiplicity of eigenvalue λ₀ is even,the bifurcation in the neighborhood of point ( 0,λ₀) take on complexity and multiplicity,so,the study towards relevant bifurcation problem bears necessity and notable meaning。In this paper,we use some theory about topological degree,combined with the LS reduction method,to make a elementary study on the steady state bifurcation of a class of 2D dynamical systems(3.1.3)in the neighborhood of point of even algebraic multiplicity eigenvalue ,gained a result of judging weather the systems exist steady state bifurcation。Though we've studied a 2D dynamical systems only,however,it means not only this。In fact,we could consider that it have resolved the similar problem of a class of higher dimensional system which could be reduced to equation(3.1.3)through the LS reduction method。...