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Determination of chaotic behaviour
Routes to chaos
Oscillators with limit cycles Van der Pols equation
Other chaotic oscillators
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amplitude approximate bifurcation diagram buckled beam chaotic attractors chaotic behaviour chaotic domain chaotic motion chaotic oscillations chaotic zone circle map coefficient compute constant criterion damping defined Definition denotes dimension dimensional Duffing's equation dynamical systems eigenvalues equation of motion equilibrium example excitation existence fixed point frequency friction given half-plane Hamiltonian homoclinic orbit Hopf bifurcation hyperbolic impact motion initial conditions integral limit cycle linear linearised loop Lorenz attractor Lyapunov exponents mechanical systems Melnikov function Melnikov method neighbourhood nonlinear nonzero obtained ordinary differential equations periodic motion periodic orbit periodic solutions perturbation phase portrait phase space Phys Poincare map Pol's equation quasiperiodically forced resonance curve rotor route to chaos saddle point shown in Fig shows small orbit solution of equation stable and unstable stochastic strange attractor strange chaotic attractors strange nonchaotic attractors subharmonic symmetrical system parameters theorem torus trajectories transverse unstable manifolds variational equation vector velocity