Analysis and simulation of chaotic systems
Designed to be used at the graduate level in applied mathematics, studying mathematical analysis and computer simulation of dynamical systems. Computations and computer simulations are used throughout to illustrate the phanomena discussed and to supply readers with probes for use on new problems. 74 illustrations.
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Oscillations of Linear Systems
Stability of Nonlinear Systems
6 other sections not shown
amplitude approach approximation asymptotically stable Averaging Theorem behavior bifurcation equations calculation change of variables Chapter coefficients components Consider the system constant construct coordinates define denote derived described determined differential equations Duffing's equation dy/dt dynamics eigenvalues equation d2x equation dx/dt example expansion exponentially fixed point forcing formula Fourier Fourier series frequency full problem Hamiltonian system Hypothesis Implicit Function Theorem initial conditions initial transient interval invariant iteration Jacobian matrix Liapunov function linear problem linear system mathematical matrix modified perturbation method nonlinear oscillations orbit ordinary differential equations oscillatory parameter pendulum periodic function periodic solution persistent disturbances perturbation problems phase variables Pol's equation proof QSSA quasiperiodic function quasistatic reduced problem regular perturbation result rotation number satisfies Section sequence shows smooth function stable under persistent static Suppose system dx/dt Taylor's theory tion torus transformation unique solution unstable manifolds VCON voltage zero