For a system of type-I neurons bidirectionally coupled through a nonlinear feedback mechanism, we discuss the issue of noise-induced complete synchronization (CS). For the inputs to the neurons, we point out that the rate of change of instantaneous frequency with the instantaneous phase of the stochastic inputs to each neuron matches exactly with that for the other in the event of CS of their outputs. Our observation can be exploited in practical situations to produce completely synchronized outputs in artificial devices. For excitatory–excitatory synaptic coupling, a functional dependence for the synchronization error on coupling and noise strengths is obtained. Finally, we report a noise-induced CS between nonidentical neurons coupled bidirectionally through random nonzero couplings in an all-to-all way in a large neuronal ensemble.

We discuss how phase-transitions may be detected in computationally hard problems in the context of anytime algorithms. Treating the computational time, value and utility functions involved in the search results in analogy with quantities in statistical physics, we indicate how the onset of a computationally hard regime can be detected and the transit to higher quality solutions be quantified by an appropriate response function. The existence of a dynamical critical exponent is shown, enabling one to predict the onset of critical slowing down, rather than finding it after the event, in the specific case of a travelling salesman problem (TSP). This can be used as a means of improving efficiency and speed in searches, and avoiding needless computations.

Nonlinear oscillations of a bubble carrying a constant charge and suspended in a fluid, undergoing periodic forcing due to incident ultrasound are studied. The system exhibits period-doubling route to chaos and the presence of charge has the effect of advancing these bifurcations. The minimum magnitude of the charge 𝑄_min above which the bubble’s radial oscillations can occur above a certain velocity 𝑐₁ is found to be related by a simple power law to the driving frequency 𝜔 of the acoustic wave. We find the existence of a critical frequency $\omega_{H}$ above which uncharged bubbles necessarily have to oscillate at velocities below $c_{1}$. We further find that this critical frequency crucially depends upon the amplitude $P_{s}$ of the driving acoustic pressure wave. The temperature of the gas within the bubble is calculated. A critical value 𝑃_tr of $P_{s}$ equal to the upper transient threshold pressure demarcates two distinct regions of 𝜔 dependence of the maximal radial bubble velocity 𝑣_max and maximal internal temperature 𝑇_max. Above this pressure, 𝑇_max and 𝑣_max decrease with increasing 𝜔, while below 𝑃_tr, they increase with 𝜔. The dynamical effects of the charge, the driving pressure and frequency of ultrasound on the bubble are discussed.