A Novel Highly Nonlinear Quadratic System: Impulsive Stabilization, Complexity Analysis, and Circuit Designing

Figure 3

Lyapunov exponents and bifurcation diagrams when value is fixed (). (a) For a range of , the two largest Lyapunov exponents are potted. Based on these Lyapunov exponents’ values, the system’s behaviors (torus when both are zero, chaos when one is zero and another is positive, and periodic when one is negative and another is zero) for each specific value of can be determined. (b) Bifurcation diagrams of the system for the ’s same range. Period-doubling route to chaos (from right side to the left) and periodic windows can be seen in the diagram.

(a)

(b)