Parameter perturbations in dynamical models of biochemical networks affect the qualitative dynamical behaviour observed in the model. Since this qualitative behaviour is in many cases the key model output used to explain biological function, the robustness analysis of the model’s behaviour with respect to parametric uncertainty is a crucial step in systems biology research. In this paper, we de...

We investigate the dynamics of a delayed nonlinear Mathieu equation: ẍ + (δ + εα cos t)x + εγ x = εβx(t − T ) in the neighborhood of δ = 1/4. Three different phenomena are combined in this system: 2:1 parametric resonance, cubic nonlinearity, and delay. The method of averaging (valid for small ε) is used to obtain a slow flow that is analyzed for stability and bifurcations. We show that the 2:1...

We study a dissipative dynamical system that models a parametric instability in a plasma. This instability is due to the interaction of a whistler with the ion acoustic wave and a plasma oscillation near the lower hybrid resonance. The amplitude of these three oscillations obey a three-dimensional system of ordinary differential equations which exhibits chaos for certain parameter values. By us...

A linear stability analysis of the parallel uniform flow in a horizontal channel with open upper boundary is carried out. The lower boundary is considered as an impermeable isothermal wall, while the open upper boundary is subject to a uniform heat flux and it is exposed to an external horizontal fluid stream driving the flow. An eigenvalue problem is obtained for the two-dimensional transverse...

A simplified model describing acoustically-generated parametric instability in a spherical chamber is developed for quasi-one-dimensional, low-Mach flames. We demonstrate how sound waves generated by a centrally-ignited, outwardly-propagating accelerating flamefront can be incorporated into a theory of self-similar flame acceleration in free space developed previously. Being reflected from the ...

Recent full hydrodynamic simulations of a sonoluminescing bubble interior have shown that the bubble content is compressed to a very dense state during the violent collapse. In this paper, we numerically studied the shape stability of a radially oscillating gas bubble by using Hilgenfeldt et al. theoretical model with corrections taking into account the gas density effect. Our results show that...

We study the response of a large array of coupled nonlinear oscillators to parametric excitation, motivated by the growing interest in the nonlinear dynamics of microelectromechanical and nanoelectromechanical systems (MEMS and NEMS). Using a multiscale analysis, we derive an amplitude equation that captures the slow dynamics of the coupled oscillators just above the onset of parametric oscilla...

We report the observation of modulation instability (MI) in the mid-infrared (mid-IR) spectral region by pumping a hybrid polymer-chalcogenide optical microwire with a femtosecond optical parametric oscillator operating at 2.6 μm. It is further shown that this MI occurs in the normal dispersion regime through negative fourth-order dispersion and leads to far-detuned parametric frequency convers...

The paper deals with comparison of two principal approaches to uncertainty modelling and related robust stability analyses for a system with uncertain time-delay. A paper bleaching process, used as a testing plant, is described first as a system with parametric uncertainty and then in the form of unstructured multiplicative uncertainty model. The robust stability or instability of closed contro...

We show that optical spring damping in an optomechanical resonator can be enhanced by injecting a phase delay in the laser frequency-locking servo to rotate the real and imaginary components of the optical spring constant. This enhances damping at the expense of optical rigidity. We demonstrate enhanced parametric damping which reduces the Q factor of a 0.1-kg-scale resonator from 1.3 105 to 6....