Research team:

- Dr. Eric (ITB)
- Marwan, MSi (PhD student, ITB)
- Livia Owen, MSi (PhD student, ITB)

Collaborator:

- Prof. H.W. Broer (Univ Groningen),
- Prof F. Verhulst (Univ Utrecht),
- Kie Van Ivanky Saputra PhD., (Universitas Pelita Harapan).
- Kus Prihantoso M.Si., (Universitas Negeri Jogjakarta)

This research was funded by:

- ITB, by Riset KK B ITB 2019.
- ITB, by Riset P3MI 2018.
- ITB, by Riset P3MI 2017.
- ITB, by Riset KK ITB 2017.
- ITB, by Riset KK ITB 2015.
- ITB, by Penguatan Riset Institusi 2011.
- KNAW (Royal the Netherlands Society for Science), by Spin PostDoctoral Program 2007.

**Two dimensional predator-prey type of dynamical system.**

We investigate a predator-prey model with a non-monotonic response function subjected to a small periodic forcing. This forcing term is chosen to model for example, the small variations in the natural growth or carrying capacity due to seasonal change in the environtment. This is investigated by using the so-called stroboscopic map.

We begin with studying the dynamics and bifurcations in the system, especially the bifurcation of periodic solution as we turn on the time periodic perturbation. There we have observed some interesting co-dimension two bifurcation for equilibria, namely: Bogdanov-Takens bifurcation, cusp bifurcation and Bautin bifurcation. As for bifurcation of periodic solution, we have observed the occurrence of Swallowtail-like bifurcation.

**Publications: **

*Published:*

- Marwan, J. M. Tuwankotta, and E. Harjanto, Application of Lagrange multiplier method for computing fold bifurcation point in a two-prey one-predator dynamical system, Journal of the Indonesian Mathematical Society, 24 (2018), pp. 7–19.
- Eric Harjanto, J.M. Tuwankotta,Bifurcation of periodic solution in a Predator-Prey type of systems with non-monotonic response function and periodic perturbation , International Journal of Nonlinear Mechanics
**85**(2016) 188-196. - Eric Harjanto, J.M. Tuwankotta, Hilangnya Dua Bifurkasi Fold Tanpa Melalui Bifurkasi Cusp pada Sistem Predator-Prey dengan Faktor Pertahanan Grup dan Gangguan Berkala, Prosiding Konferensi Nasional Matematika XVII-2014, 11-14 Juni 2014, ITS, Surabaya.

*To appear*:

- L. Owen and J. Tuwankotta, Computation of cusp bifurcation point in a two-prey one predator model using lagrange multiplier method, in Proceedings of the International Conference on Applied Physics and Mathematics 2019, Chulalongkorn University, Bangkok, Thailand, 2019.
- Marwan, J.M. Tuwankotta, Infinitely many equilibria and some codimension one bifurcations in a subsystem of a two-prey one-predator dynamical system, Proceedings of International Conference on Mathematics and Natural Sciences, 2018, Institut Teknologi Bandung.