My research interest is in the theory and applications of dynamical systems:
- Hamiltonian dynamical systems using the normal form theory. We studied the relation between resonances, especially the higher-order ones, with the dynamics of the system. One of our main findings is the size of the resonance domain for two degrees of freedom system. The resonance domain is a domain in phase-space where interaction between the degree of freedom occurs. This usually represented by energy exchange. We have refined the size by providing sharper estimates from the one in the literature. The work is published in SIAM Journal on Applied Mathematics (see Publications page).
- Singularly perturbed conservative system.
We study linear oscillations having widely separated frequencies. These oscillations is nonlinearly coupled in such a way that the nonlinearity produces no energy input nor dissipation. This is summarized by saying that the nonlinearity preserves distance to the origin (which is a measure of energy). We add weak linear dissipation is included to the system to create instability of the trivial equilibrium. Using a combination of analytical and numerical exploration we try to described the dynamics and bifurcations in the system. The project is funded by Riset KK ITB 2006 and Riset International ITB 2007.
- Dynamics and bifurcations in predator-prey type of systems. In this research we study a predator-prey type of system which is periodically perturbed. The unperturbed system has non monotonic response function, which models the influence of group defense among the prey. One of the questions we ask is on the Bodanov-Takens point as the periodic perturbation is turned on. Currently Eric Haryanto (PhD student, ITB) and Kus Prihastono S.Si are working on this subject.
- Discrete dynamical systems: dynamics, bifurcations and integrability.