phenomenon 32.35 Self-sustained oscillation

open in the book · parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:807 · p. 1090

phenomenon-tested: no experiment declares a \tests edge to it and it is not listed in untested.txt

Rests on

depends_on definition 32.29 Limit cycle ¶
- depends_on corollary 32.5 Trajectories do not cross ¶
  - depends_on proposition 32.4 The flow is a one-parameter group ¶
    - depends_on definition 32.3 Dynamical system, phase space, flow ¶
      - depends_on definition 13.82 Vector field ¶
      - depends_on definition 9.1 Ordinary differential equation ¶
    - depends_on theorem 9.8 Picard–Lindelöf ¶
      - depends_on definition 9.4 Lipschitz condition ¶
      - depends_on equation 9.3 eq:slt-ode-system ¶
      - depends_on lemma 9.6 Weierstrass $M$-test; uniform limits are continuous ¶
      - proves proof ch:07-odes-sturm-liouville@proof-2 ¶
    - proves proof ch:15-nonlinear-dynamics-chaos@proof-1 ¶
  - depends_on theorem 9.8 Picard–Lindelöf ¶ ↺
  - proves proof ch:15-nonlinear-dynamics-chaos@proof-2 ¶
- depends_on definition 32.8 Attractor and basin ¶
  - depends_on definition 32.3 Dynamical system, phase space, flow ¶ ↺
  - depends_on definition 6.9 Compact set ¶
    - depends_on definition 6.5 Open cover ¶
      - depends_on definition 6.2 Open set ¶
      - depends_on equation 3.51 eq:set-indexed ¶
depends_on equation 32.10 eq:chaos-vdp-si ¶
proves proof ch:15-nonlinear-dynamics-chaos@proof-12 ¶

Supports

depends_on phenomenon 32.37 Frequency demultiplication and the first heard chaos ¶
- depends_on definition 32.91 The circle map ¶
  - depends_on proposition 32.93 The circle map loses invertibility at $K=1$ ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`cites`	→	LXXXVIII.On ``relaxation-oscillations''	derived	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:813
`cites`	→	LXXXVIII.On ``relaxation-oscillations''	derived	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:821
`depends_on`	→	Limit cycle	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:822
`depends_on`	→	eq:chaos-vdp-si	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:822
`depends_on`	←	Frequency demultiplication and the first heard chaos	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:936
`proves`	←	ch:15-nonlinear-dynamics-chaos@proof-12	declared	parts/03-classical-mechanics/15-nonlinear-dynamics-chaos.tex:825