Bifurcations and control studies in Circadian Rhythms in Drosophila

Bifurcation analysis and Multiobjective Nonlinear Model Predictive Control (MNLMPC) calculations were performed on a model of circadian oscillations of the period (PER) and timeless (TIM) proteins in Drosophila. The MATLAB program MATCONT was used to perform the bifurcation analysis. The optimization language PYOMO was used along with the state-of-the-art global optimization solvers IPOPT and BARON for the MNLMPC calculations. The bifurcation analysis revealed oscillation causing Hopf bifurcations while the MNLMPC calculations revealed the existence of spikes in the control profiles. Both Hopf bifurcation points and the control profile spikes were eliminated using an activation factor involving the hyperbolic tangent function.