HomMap is a library of Fortran routines to AUTO97 or AUTO94 for detection and continuation of homoclinic (and heteroclinic) points to periodic orbits and their bifurcations for maps. If the stable manifold or the unstable manifold is of dimension one, then the software can search homoclinic (or heteroclinic) points and users do not have to know their locations in advance. Periodically forced systems can also be analyzed with the Poincare maps. In addition, local bifurcation analysis for periodically forced systems can be more easily performed with HomMap than only with AUTO. A new version by which homoclinic orbits for periodic orbits in autonomous systems can be analyzed is coming soon.
HomMap requires that AUTO97 or AUTO94 is installed, and it does not run under AUTO86 and AUTO2000.
| Keywords | Bifurcation analysis, Continuation |
| Model | |
| Software Type | |
| Language | |
| Platform | |
| Availability | |
| Contact Person | Kazuyuki Yagasaki (yagasaki at ie.niigata-u.ac.jp) |
| References to Papers | 1. K. Yagasaki, "Numerical detection and continuation of homoclinic points and their bifurcations for maps and periodically forced systems," Int. J. Bifurcation Chaos, 8 (1998), 1617-1627.
2. K. Yagasaki, "Detection of homoclinic bifurcations in resonance zones of forced oscillators," Nonlinear Dynamics, 28 (2002), 285-307. |