• J Balakrishnan

      Articles written in Pramana – Journal of Physics

    • Complete synchronization in coupled type-I neurons

      Nishant Malik B Ashok J Balakrishnan

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      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.

    • Oscillatory dynamics of a charged microbubble under ultrasound

      Thotreithem Hongray B Ashok J Balakrishnan

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      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 𝑄min 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 𝑃tr of $P_{s}$ equal to the upper transient threshold pressure demarcates two distinct regions of 𝜔 dependence of the maximal radial bubble velocity 𝑣max and maximal internal temperature 𝑇max. Above this pressure, 𝑇max and 𝑣max decrease with increasing 𝜔, while below 𝑃tr, they increase with 𝜔. The dynamical effects of the charge, the driving pressure and frequency of ultrasound on the bubble are discussed.

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