Continuation techniques and interactive software for bifurcation analysis of ODEs and iterated maps. We present a numerical technique for the analysis of local bifurcations which is based on the continuation of structurally unstable invariant sets in a suitable phase-parameter space. The invariant sets involved in our study are equilibrium points and limit cycles of autonomous ODEs, periodic solutions of time-periodic nonautonomous ODEs, fixed points and periodic orbits of iterated maps. The more general concept of a continuation strategy is also discussed. It allows the analysis of various singularities of generic systems and of their mutual relationships. The approach is extended to codimension three singularities. We introduce several bifurcation functions and show how to use them to construct well-posed continuation problems. The described continuation technique is supported by an interactive graphical program called LOCBIF. We discuss briefly the concepts of the LOCBIF interface and give some examples of typical applications.
Keywords for this software
References in zbMATH (referenced in 65 articles )
Showing results 61 to 65 of 65.
- Kuznetsov, Yu. A.; Piccardi, C.: Bifurcation analysis of periodic SEIR and SIR epidemic models (1994)
- Kuznetsov, Yuri A.; Piccardi, Carlo: Bifurcations and chaos in a periodically forced prototype adaptive control system (1994)
- Gyllenberg, Mats; Söderbacka, Gunnar; Ericsson, Stefan: Does migration stabilize local population dynamics? Analysis of a discrete metapopulation model (1993)
- Khibnik, Alexander I.; Kuznetsov, Yuri A.; Levitin, Victor V.; Nikolaev, Eugene V.: Continuation techniques and interactive software for bifurcation analysis of ODEs and iterated maps (1993)
- Khibnik, Alexander I.; Borisyuk, Roman M.; Roose, Dirk: Numerical bifurcation analysis of a model of coupled neural oscillators (1992)