Janaki Balakrishnan

• National Institute of Advanced Studies

The oceans act as major carbon dioxide sinks, greatly influencing global climate. Knowing how these sinks evolve would advance our understanding of climate dynamics. We construct a conceptual box model for the oceans to predict the temporal and spatial evolution of CO2 of each ocean, and the time-evolution of their salinities. Surface currents, dee...

Increased levels of greenhouse gases in the atmosphere, especially carbon dioxide, are leading contributors to a significant increase in the global temperature, and the consequent global climatic changes are more noticeable in recent years than in the past. A persistent increased growth of such gases might lead to an irreversible transition or tipp...

Capturing movement of animals in mathematical models has long been a keenly pursued direction of research ¹ . Any good model of animal movement is built upon information about the animal’s environment and the available resources including whether prey is in abundance or scarce, densely distributed or sparse ² . Such an approach could enable the ide...

The adiabatic invariance of the action variable of a length varying pendulum is investigated in terms of the two different time scales that are associated with the problem. A length having a general polynomial variation in time is studied; an analytical solution for a pendulum with length which varies quadratically in time is obtained in the small...

The rich dynamics of a system comprising of a Type-I neuron coupled to a Type-II neuron via an electrical synapse (gap junction) are explored in this paper. Diverse dynamical behaviour ranging from quiescence and periodic spiking, to bursting and burst synchronization, were observed for different coupling schemes. The bifurcation mechanisms underly...

q-deformations of functions and distributions have been used in the literature to explain several experimental observations. In this work, we study the dynamics of the Tinkerbell map under q-deformations. The system exhibits a rich variety of dynamical behavior as q varies, including occurrences of interior crises, paired cascades, simultaneous occ...

A detailed study is performed on the parameter space of the mechanical system of a driven pendulum with damping and constant torque under feedback control. We report an interesting bow-tie shaped bursting oscillatory behaviour, which is exhibited for small driving frequencies, in a certain parameter regime, which has not been reported earlier in th...

We study the dynamics of a discrete-time tritrophic model which mimics the observed periodicity in the population cycles of the larch budmoth insect which causes widespread defoliation of larch forests at high altitudes periodically. Our model employs q-deformation of numbers to model the system comprising the budmoth, one or more parasitoid specie...

Periodic outbreaks of the larch budmoth Zeiraphera diniana population (and the massive forest defoliation they engender) have been recorded in the Alps over the centuries and are known for their remarkable regularity. But these have been conspicuously absent since 1981. On the other hand, budmoth outbreaks have been historically unknown in the larc...

We report an interesting bow-tie shaped bursting behaviour in a certain parameter regime of two resistive-capacitative shunted Josephson junctions, one in the oscillatory and the other in the excitable mode and coupled together resistively. The burst emerges in both the junctions and they show near-complete synchronization for strong enough couplin...

We present here some studies on noise-induced order and synchronous firing in a system of bidirectionally coupled generic type-I neurons. We find that transitions from unsynchronized to completely synchronized states occur beyond a critical value of noise strength that has a clear functional dependence on neuronal coupling strength and input values...

In any organism there are different kinds of sensory receptors for detecting the various, distinct stimuli through which its external environment may impinge upon it. These receptors convey these stimuli in different ways to an organism’s information processing region enabling it to distinctly perceive the varied sensations and to respond to them....

The concept of q-deformation of numbers is applied here to improve and modify a tritrophic population dynamics model to understand defoliation of the coniferous larch trees due to outbreaks of the larch bud-moth insect population. The results are in qualitative agreement with observed behavior, with the larch needle lengths, bud-moth population and...

The effect of charge on the dynamics of a gas bubble undergoing forced oscillations in a liquid due to incidence of an ultrasonic wave is theoretically investigated. The limiting values of the possible charge a bubble may physically carry are obtained. The presence of charge influences the regime in which the bubble's radial oscillations fall. The...

Organisms endowed with life show a sense of awareness, interacting with and learning from the universe in and around them. Each level of interaction involves transfer of information of various kinds, and at different levels. Each thread of information is interlinked with the other, and woven together, these constitute the universe - both the intern...

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 ra...

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 ra...

We emphasize here the role of the Hopf bifurcation in detection of stimuli in sensory processes--we discuss in particular chemosensors. It is shown that the essential nonlinearities inherent in the signal transduction mechanism can take advantage of the noise from the environment the system is subject to, to display a highly amplified response to s...

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 t...

We present here some studies on noise-induced order and synchronous firing in a system of bidirectionally coupled generic type-I neurons. We find that transitions from unsynchronized to completely synchronized states occur beyond a critical value of noise strength that has a clear functional dependence on neuronal coupling strength and input values...

The process of hearing can be understood as one arising through the action of a number of nonlinear elements operating near dynamical instabilities in an environment subject to fluctuations. The sound detector in the inner ear, the mechanoelectrical transducer hair cell can be modelled as a forced Hopf oscillator. When such a system is additionally...

A geometric approach is introduced for understanding the phenomenon of phase synchronization in coupled nonlinear systems in the presence of additive noise. We show that the emergence of cooperative behavior through a change of stability via a Hopf bifurcation entails the spontaneous appearance of a gauge structure in the system, arising from the e...

The problem of self-tuning a system to the Hopf bifurcation in the presence of noise and periodic external forcing is discussed. We find that the response of the system has a non-monotonic dependence on the noise-strength, and displays an amplified response which is more pronounced for weaker signals. The observed effect is to be distinguished from...

A path-integral formalism is proposed for studying the dynamical evolution in time of patterns in an artificial neural network in the presence of noise. An effective cost function is constructed which determines the unique global minimum of the neural network system. The perturbative method discussed also provides a way for determining the storage...

Group theoretical concepts are invoked in a specific model to explain how only twenty amino acids occur in nature out of a possible sixty four. The methods we use enable us to justify the occurrence of the recently discovered 21st amino acid selenocysteine, and also enables us to predict the possible existence of two more, as yet undiscovered amino...

. The method of stochastic quantization of Parisi–Wu is extended to include spinor fields obeying the generalized statistics of order two consistent with the weak locality requirement. Appropriate Langevin and Fokker–Planck equations are constructed using paragrassmann variables, which give rise to two fields with different masses in the equilibriu...

We show that the time-dependent version of Sato's equation, when applied to capacitative radio frequency sheaths, is no longer independent of the electric field of the space charge, and we discuss the use of the equation for a specific sheath model.

For a substance diffusing on a curved surface, we obtain an explicit relation valid for very small values of the time, between the local concentration, the diffusion coefficient, the intrinsic spatial curvature, and the time. We recover the known solution of Fick's law of diffusion in the flat space limit. In the biological context, this result wou...

We calculate the effective potential for a gauged scalar field theory with minimal coupling to gravity, in (2 + 1)-dimensional curved spacetime using mean-field-theory approximation techniques. Gauge independence of the off-shell effective action is ensured by working within the framework of the Vilkovisky-DeWitt approach.

We obtain high temperature results for the one-loop effective action for composite fields in interaction with an Abelian gauge field and minimally coupled to gravity in a curved background space-time, using the Vilkovisky-DeWitt approach, by making a local expansion in the Riemann tensor and its derivatives. We also give results for the fields mini...

It is shown that improved potentials and corrected mass terms can be introduced by using a quadratic source term in the path integral construction for the effective action. The advantage of doing things this way is that we avoid ever having to deal with complex propagators in the loop expansion. The resulting effective action for electroweak phase...

We calculate the effective potential to one-loop order for scalar and spinor fields minimally coupled to gravity by making a local expansion in powers of the curvature. Our calculations are done in the unitary gauge to third order in the Riemann tensor, using the geometrical background field method of Vilkovisky and DeWitt. The final result is gaug...

We calculate the one-loop effective action for scalar and spinor electrodynamics in euclidean de Sitter space in the unitary gauge using the covariant Vilkovisky-DeWitt procedure. The resulting effective action is gauge independent. Our calculations are performed to third order in the Riemann tensor, and disagree with those of other authors obtaine...

We enumerate the advantages of using the stochastic quantization method over the standard methods and as an example use it to quantize para-Fermi fields obeying trilinear quantum conditions. Finally chiral anomaly for spinor fields is obtained directly from thec-number Langevin equation which forms the basis of the stochastic approach for field qua...

The application of the method of stochastic quantization originally attributed to Parisi and Wu has been extended to spinor fields obeying para‐Fermi statistics. The connection between Euclidean and stochastic field theories is established in the conventional manner by proving the equivalence between a Langevin equation satisfied by para‐Grassmann...

We obtain a generalization of Fujikawa's result on the chiral anomaly for spinor fields obeying para-Fermi statistics of order p. This is done within the context of Parisi-Wu stochastic quantization extended to parafermion spinor fields. For p = 1, we recover the standard result for an ordinary Fermi field.

We discuss the problem of tuning an externally forced, noisy nonlinear system to operate close to a Hopf bifurcation. We find that the response of the system has a non-monotonic dependence on the noise- strength, and displays an amplified response which is more pronounced for weaker signals. The observed effect is to be distinguished from stochas-...

We study synchronous activity in a system of coupled excitatory and inhibitory Class-I neurons having unidirectional as well as bidirectional couplings. We show that addition of Gaussian white noise induces synchronization in both phase & frequency, and also the system exhibits windows of complete synchronization. In the absence of an external inpu...