Explaining observations in the population dynamics of ecosystems influenced by the environment and being able to correctly predict future events in these complex systems is one of the major challenges in mathematical modelling. We present our models having climate parameters which explain experimental observations of the cyclic population dynamics of the larch budmoth – an insect pest which causes massive defoliation of entire larch forests at high altitudes around the world. The tritrophic ecological system consists of the larch trees, the budmoth and parasitoid species which live off the budmoths. We make an important modification of the models we had proposed earlier by incorporating a slow time dependence in one of the species-specific parameters, in order to provide an explanation for the irregular larch budmoth cyclic outbreaks observed in the French Alps.

PACS Nos 05.45.-a; 05.45.Pq; 87.23.Cc

The nonlinear, forced oscillations of a bubble in a fluid due to an external pressure field are studied theoretically. In the presence of a constant charge on the bubble, the bubble oscillator’s behaviour changes markedly. We report results at significantly higher pressures and forcing frequencies than presented earlier. The influence of the bubble’s ambient radius on thresholds and dynamics is also reported. Charge and pressure thresholds are calculated for the system, delineating different dynamics.

PACS Nos 05.45.-a; 05.90.+m

We present an overview of our studies on some simple mechanical systems including the ‘simple’ nonlinear pendulum and its variants. We show that these systems exhibit numerous types of regular bursting oscillations which are seen in biological neurons. In particular, we discuss bow-tie shaped bursts which we foundin a driven pendulum with linear velocity damping, under constant torque and dynamic feedback. Similar bursts of identical bow-tie shape have been reported by us previously in a system of two resistively coupled Josephson junctions in a certain parameter regime under certain conditions. We discuss the bifurcation mechanism producing some of these bursts.