Analysis Of Bogdanov-Takens Bifurcation And Chaos In Chua Circuit

Generally speaking,chaos,bifurcation,fractal and complexity are the main contents of nonlinear science,and its research results are applied in various fields,especially in secure communication,system security,ecological environment and so on.This dissertation mainly studies the dynamics behaviors including bifurcations and chaos phenomena in Chua's system by two different methods.For the first method,we explicitly calculate the center manifold corresponding to the Bogdanov-Takens(BT)bifurcation by using the center manifold theorem.Then we obtain the normal form and universal unfolding of BT bifurcation.We get the corresponding bifurcation structures in Chua's system and plot its bifurcation diagrams and phase portraits eventually.For the second method,by using the homologous algebra theory,we get the homologous equation corresponding to the BT bifurcation in Chua's system.Then we establish the linear algebraic equations that the coefficients of normal form and parameters of universal unfolding are satisfied with.Finally we obtain the normal form,universal unfolding and bifurcation structures of BT bifurcation.In the end of this dissertation,we verify that the chaotic phenomena do exist in Chua's system by evaluating its Lyapunov exponential spectrum.