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Continuation of codim 1 bifurcations

MATCONT computes branches of codim 1 bifurcations of equilibria (namely, fold LP and Hopf H) and of limit cycles (fold of cycles LPC, period doubling PD and Neimark-Sacker NS). On these branches codimension 2 bifurcations of equilibria (CP,BT,ZH,HH,GH) and of limit cycles (CPC,R1,R3,R4,CH,LPNS,PDNS,R2, NSNS,LPPD and GPD) are detected and located, cf. the graph of adjacency in Figure 1.1. For the numerical methods used in the computation of the normal form coefficients, but also for the meaning and use of these coefficients we refer to [25] in the equilibrium case and to [9] in the limit cycle case. We note that the MATCONT directory `LimitCycleCodim2` is exclusively devoted to the computation of normal form coefficients of codim 2 bifurcations of limit cycles.

Subsections

- Fold Continuation
  - Mathematical definition
  - Bifurcations along a fold curve
  - Fold initialization
  - Adaptation
  - Example: a catalytic oscillator
- Hopf Continuation
  - Mathematical definition
  - Bifurcations along a Hopf curve
  - Hopf initialization
  - Adaptation
  - Example
- Period Doubling
  - Mathematical definition
  - Output of a continuation of period doubling bifurcation points
  - Bifurcations along a flip curve
  - Period doubling initialization
  - Example
- Continuation of fold bifurcation of limit cycles
  - Mathematical definition
  - Bifurcations along a fold of cycles curve
  - Fold of cycles initialization
  - Example: the fast Morris-Lecar equations
- Continuation of torus bifurcation of limit cycles
  - Mathematical definition
  - Bifurcations along a Neimark-Sacker curve
  - Torus bifurcation initialization
  - Example: an autonomous electronic circuit