Nonlinear Dynamics and ChaosJohn Wiley & Sons, 15. feb. 2002 - 464 sider Nonlinear dynamics and chaos involves the study of apparent random happenings within a system or process. The subject has wide applications within mathematics, engineering, physics and other physical sciences. Since the bestselling first edition was published, there has been a lot of new research conducted in the area of nonlinear dynamics and chaos.
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Indhold
Introduction | 1 |
An overview of nonlinear phenomena | 15 |
Point attractors in autonomous systems | 26 |
Limit cycles in autonomous systems | 50 |
Periodic attractors in driven oscillators | 62 |
Chaotic attractors in forced oscillators | 80 |
Stability and bifurcations of equilibria and cycles | 106 |
Stability and bifurcation of maps | 135 |
The Lorenz system | 207 |
Rösslers band | 229 |
Geometry of bifurcations | 249 |
Subharmonic resonances of an offshore structure | 285 |
Chaotic motions of an impacting system | 302 |
Escape from a potential well | 313 |
Appendix | 359 |
| 402 | |
Chaotic behaviour of one and twodimensional maps | 161 |
The geometry of recurrence | 183 |
Online Resources | 428 |
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Almindelige termer og sætninger
amplitude asymptotic basin boundary basin of attraction cascade catastrophe centre manifold chaos chaotic attractor chaotic motions Chapter codimension complex control parameter curve cyclic fold damping diagram differential equations dimension dissipative divergence Duffing's equation dynamical system eigenvalues eigenvector equilibrium point example fixed point flip bifurcation flow forced oscillators forcing cycle forcing frequency fractal global bifurcation Guckenheimer Hénon map heteroclinic Holmes homoclinic connection Hopf bifurcation illustrated initial conditions inset invariant manifolds iterations jump Lett Liapunov limit cycle logistic map Lorenz system Math mathematical nearby trajectories Neimark node nonlinear dynamics nonlinear oscillator observed one-dimensional maps outset path pendulum period-doubling periodic orbits perturbation phase portrait phase space Phys plane Poincaré mapping Poincaré section qualitative resonance saddle cycle saddle point saddle-node bifurcation sequence shown in Figure Smale solution spiral stable manifold starting steady steady-state structurally stable subcritical subharmonic supercritical Thompson topological transient two-dimensional typical Ueda undamped unstable values vector field zero