A Study of Double Hopf Bifurcations and Collective Dynamics of Nonlinear Networks with Time Delay
DescriptionTo realistically model physical and biological systems with interactions, the influence of past states generally needs to be taken into account. Such systems can be modelled by a set of delay differential equations (DDEs). The study of double Hopf bifurcation in DDEs has attracted much attention as this type of bifurcation gives birth to various solutions. However, using the current method of centre manifold reduction (CMR) for the study of such bifurcations is tedious. An innovative integration method recently proposed by the researchers will be applied to study these bifurcations in some popular nonlinear models and investigate their physical significance.In a nonlinear network, time delay in reactions among the nodes often creates complicated behaviour that cannot be predicted from the dynamics of individual nodes. The researchers will apply a perturbation-increment (PI) scheme to analyze the collective dynamics of a network due to one or more delayed feedbacks. Such an investigation will lead to a deeper understanding of the mechanism that time delay and network topology play in relation to various complex phenomena such as synchronization, periodic bursting, and spiking. This investigation is also vital to control design as it will provide appropriate control strategy to achieve specific goals.
|Effective start/end date||1/09/07 → 11/05/11|