Bifurcations and Chaos in Piecewise-smooth Dynamical Systems
Technical problems often lead to differential equations withpiecewise-smooth right-hand sides. Problems in mechanicalengineering, for instance, violate the requirements of smoothness ifthey involve collisions, finite clearances, or stickOCoslipphenomena."
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amplitude analysis arise basin of attraction Baushev behavior Bifurcation and Chaos bifurcation curve bifurcation diagram bifurcation point border-collision bifurcations boundary branching pattern chaotic attractor chaotic dynamics chaotic oscillations Chapter circuit coexisting complex consider corresponding DC/DC converters deadzone denote domains of existence dynamical system eigenvalues feedback Figure finite fixed point Henon map homoclinic Hopf bifurcation hyperchaotic hysteresis illustrated initial conditions intersect intervals limit cycle logistic map Lyapunov exponent m-cycle matrix modes Mosekilde motor multipliers Nonlinear Dynamics observed output parameter values period-2 cycle period-doubling bifurcations periodic motion periodic orbit periodic solutions phenomena Phys piecewise linear piecewise-smooth Poincare Power Electronics pulse pulse-width modulation quasiperiodic motion regions relay control systems relay element relay system resonance cycle saddle cycle saddle-node bifurcation sensor sequence shown in Fig shows structure switching synchronization tion torus transition to chaos two-dimensional torus unstable cycles unstable manifold voltage Zhusubaliyev