arXiv subjects

Indranil Ghosh

Publications and source records attributed to Indranil Ghosh.

At least 19 recordsLinked to original sources

arXiv2026

Dynamical Consequences of Nontrivial Topology of Molecular Conical Intersections

The topology of the electronic structure for an avoided crossing and a conical intersection (CI) is different and is characterized by the presence of the geometric phase in the electronic wavefunction in the latter. Using the linear Jahn-Teller model, we show that an avoided crossing can be created from the conical intersection while preserving the nontrivial topology of the latter by adding a Pauli $\sigma_y$ term to the Hamiltonian. Analogously to solid state systems, we derive a half-integer topological invariant as the integral of the Berry curvature over the CI nuclear branching space. We investigate the influence of electronic topology on chemical dynamics by conducting fewest-switches surface hopping simulations and find distinct hopping rates on identical eigensurfaces but with different topologies. Our work extends the influence of topology on molecular excited state dynamics beyond the Berry phase that can be practically realized through electron-nuclear and spin-orbit coupling.

physics.chem-ph↗

arXiv2026

Stochastic Spatial Metapopulation Modelling of HPAI Control and Poultry Restocking on Jolly Island

Highly pathogenic avian influenza (HPAI) outbreaks require rapid control during active transmission and evidence-based decisions on the safe restocking of depopulated farms. We developed a stochastic spatial SEIR-based metapopulation model for a synthetic HPAI outbreak on the fictional Jolly Island. Farms were classified as `Broiler-2', `organic duck', or `Other' production systems. The model incorporated local, environmental, movement-mediated, and distance-dependent transmission, together with reactive and preventive culling, production-specific confinement, and capacity-based restocking. The simulated epidemic was geographically concentrated and differed substantially among production classes. Preventive culling reduced mean cumulative burden from 16,362.7 to 13,631.9 infectious-farm-days, with an overall reduction of 16.7\%. Earlier confinement substantially reduced epidemic magnitude, while stronger environmental transmission increased the epidemic peak. Restocking risk declined as the epidemic approached resolution. Under the model assumptions, 24 May 2026 was the first candidate date satisfying the predefined rebound-probability threshold of 0.20. For restocking on 15 March 2026, none of the tested restocking fractions met this criterion. Capacity-based restocking reduced cumulative burden by 8.45\% and rebound probability from 0.780 to 0.533, compared with restocking relative to the baseline population. These findings demonstrate the value of integrating epidemic control and post-outbreak recovery within a single modelling framework. Timely confinement, targeted preventive culling, and phased capacity-based restocking may reduce both epidemic burden and resurgence risk, although operational decisions should also incorporate surveillance, biosecurity, economic considerations, and regulatory requirements.

q-bio.PE↗

arXiv2026

Collective Phase Reorganization and Cluster Synchronization in Networks of Coupled Gumowski--Mira Maps

We investigate the collective dynamics of networks composed of diffusively coupled Gumowski-Mira maps and analyze how modifications in the intrinsic dynamics of the local oscillator reorganize the emergent phase structure of the network. The coupling strength and the local control parameter are treated as bifurcation parameters, and the resulting collective states are quantified using the largest Lyapunov exponent, a synchronization error measure, cluster-count statistics, and collective phase-classification diagrams. Two representative regimes of the local dynamics are examined. In the first regime, the network exhibits a smooth and highly organized collective parameter space, featuring a synchronization wedge embedded within an extended region of periodic cluster states. In the second regime, the same coupling architecture yields a fragmented phase organization, comprising disconnected synchronization islands, incoherent domains, and enhanced chaotic-cluster states. These results indicate that variations in the intrinsic dynamics of the individual Gumowski-Mira oscillator do not simply shift synchronization thresholds but can fundamentally restructure the topology of the collective phase space. Our findings thus establish a direct relationship between local nonlinear dynamics and the emergent organization of collective phases in coupled discrete-time networks.

math.DS↗

arXiv2026

Resonant grazing bifurcations revisited

In vibro-impact mechanics, the division between an impact and a near miss is a zero-velocity grazing event. Grazing bifurcations of stable periodic motions often produce complicated attractors when grazing generates a square-root term in the Poincar\'e map. This paper concerns codimension-two scenarios for which the square-root term vanishes in some iterate of the Poincar\'e map. For forced one-degree-of-freedom oscillators, this occurs when the forcing frequency is a certain rational multiple of the damped natural frequency, i.e., the system is in resonance. In two-parameter bifurcation diagrams, curves of saddle-node and period-doubling bifurcations of single-impact periodic motions emanate from the codimension-two points. In this paper we prove these curves are quadratically tangent to the curve of grazing bifurcations, and derive explicit formulas for their quadratic coefficients. This is achieved by modifying the Poincar\'e map in a way that circumvents the square-root singularity, enabling us to use the implicit function theorem to demonstrate smoothness and perform asymptotic calculations of the saddle-node and period-doubling bifurcation curves. In doing so we resolve a long-standing conjecture on the admissibility of single-impact periodic motions by supplementing raw asymptotic computations with geometric and topological arguments. We illustrate the results with a linear impact oscillator model, matching the theoretical unfolding to numerically computed bifurcation curves. The results explain why previously reported physical experiments reveal an absence of chaos shortly past the grazing bifurcation.

math.DS↗

arXiv2025

The VIVID function for numerically continuing periodic orbits arising from grazing bifurcations of hybrid dynamical systems

Periodic orbits of systems of ordinary differential equations can be found and continued numerically by following fixed points of Poincar\'e maps. However, this often fails near grazing bifurcations where a periodic orbit collides tangentially with a boundary of phase space. Failure occurs when the map contains a square-root singularity and the root-finding algorithm searches beyond the domain of viable values. We show that by instead following the zeros of a function that maps Velocity Into Variation In Displacement (VIVID) this issue is circumvented and there is no such failure. We illustrate this with a prototypical one-degree-of-freedom impact oscillator model by applying Newton's method to the VIVID function to follow periodic orbits collapsing into grazing bifurcations. We also follow curves of saddle-node and period-doubling bifurcations of periodic orbits that issue from a codimension-two resonant grazing bifurcation. The VIVID function provides a simple alternative to the more sophisticated collocation method and enables periodic orbits and their bifurcations to be resolved easily and accurately near grazing bifurcations.

math.DS↗

arXiv2025

Time series analysis of coupled slow-fast neuron models: From Hurst exponent to Granger causality

We perform time series analysis of small networks where every node is the slow-fast version of the denatured Morris--Lecar neuron proposed by Schaeffer and Cain. We choose popular coupling strategies from the literature and provide a detailed account of how varying their strength drives the dynamics of the small networks. Algorithms for time series analysis range from measuring their persistence (ability to remember past values), irregularity, chaos and quasiperiodicity, to synchronization between time series from every node within a network. Chaos is observed for inhibitory coupling strengths and for temperature higher than a reference temperature when the coupling is thermally sensitive. We observe quasi-periodicity when the coupling is very weak and synchronized bursting for highly excitatory coupling strength. In certain cases we also observe decay oscillations. Finally, a causality test is performed to detect whether the dynamics of one neuron is influencing the dynamics of the other in the coupled system.

nlin.CD↗

arXiv2025

A Bivariate Poisson-Gamma Distribution: Statistical Properties and Practical Applications

Although the specification of bivariate probability models using a collection of assumed conditional distributions is not a novel concept, it has received considerable attention in the last decade. In this study, a bivariate distribution-the bivariate Poisson-Gamma conditional distribution-is introduced, combining both univariate continuous and discrete distributions. This work explores aspects of this model's structure and statistical inference that have not been studied before. This paper contributes to the field of statistical modeling and distribution theory through the use of maximum likelihood estimation, along with simulations and analyses of real data.

stat.ME↗

arXiv2025

Fractional order induced bifurcations in Caputo-type denatured Morris-Lecar neurons

We set up a system of Caputo-type fractional differential equations for a reduced-order model known as the {\em denatured} Morris-Lecar (dML) neurons. This neuron model has a structural similarity to a FitzHugh-Nagumo type system. We explore both a single-cell isolated neuron and a two-coupled dimer that can have two different coupling strategies. The main purpose of this study is to report various oscillatory phenomena (tonic spiking, mixed-mode oscillation) and bifurcations (saddle-node and Hopf) that arise with variation of the order of the fractional operator and the magnitude of the coupling strength for the coupled system. Various closed-form solutions as functions of the system parameters are established that act as the necessary and sufficient conditions for the stability of the equilibrium point. The theoretical analysis are supported by rigorous numerical simulations.

math.DS↗

arXiv2024

Robust chaos in $\mathbb{R}^n$

We treat $n$-dimensional piecewise-linear continuous maps with two pieces, each of which has exactly one unstable direction, and identify an explicit set of sufficient conditions for the existence of a chaotic attractor. The conditions correspond to an open set within the space of all such maps, allow all $n \ge 2$, and allow all possible values for the unstable eigenvalues in the limit that all stable eigenvalues tend to zero. To prove an attractor exists we use the stable manifold of a fixed point to construct a trapping region; to prove the attractor is chaotic we use the unstable directions to construct an invariant expanding cone for the derivatives of the pieces of the map. We also show the chaotic attractor is persistent under nonlinear perturbations, thus when such an attractor is created locally in a border-collision bifurcation of a general piecewise-smooth system, it persists and is chaotic for an interval of parameter values beyond the bifurcation.

nlin.CD↗

arXiv2024

Dynamical properties of a small heterogeneous chain network of neurons in discrete time

We propose a novel nonlinear bidirectionally coupled heterogeneous chain network whose dynamics evolve in discrete time. The backbone of the model is a pair of popular map-based neuron models, the Chialvo and the Rulkov maps. This model is assumed to proximate the intricate dynamical properties of neurons in the widely complex nervous system. The model is first realized via various nonlinear analysis techniques: fixed point analysis, phase portraits, Jacobian matrix, and bifurcation diagrams. We observe the coexistence of chaotic and period-4 attractors. Various codimension-1 and -2 patterns for example saddle-node, period-doubling, Neimark-Sacker, double Neimark-Sacker, flip- and fold-Neimark Sacker, and 1:1 and 1:2 resonance are also explored. Furthermore, the study employs two synchronization measures to quantify how the oscillators in the network behave in tandem with each other over a long number of iterations. Finally, a time series analysis of the model is performed to investigate its complexity in terms of sample entropy.

nlin.AO↗

arXiv2024

On the higher-order smallest ring star network of Chialvo neurons under diffusive couplings

We put forward the dynamical study of a novel higher-order small network of Chialvo neurons arranged in a ring-star topology, with the neurons interacting via linear diffusive couplings. This model is perceived to imitate the nonlinear dynamical properties exhibited by a realistic nervous system where the neurons transfer information through higher-order multi-body interactions. We first analyze our model using the tools from nonlinear dynamics literature: fixed point analysis, Jacobian matrix, and bifurcation patterns. We observe the coexistence of chaotic attractors, and also an intriguing route to chaos starting from a fixed point, to period-doubling, to cyclic quasiperiodic closed invariant curves, to ultimately chaos. We numerically observe the existence of codimension-1 bifurcation patterns: saddle-node, period-doubling, and Neimark Sacker. We also qualitatively study the typical phase portraits of the system and numerically quantify chaos and complexity using the 0-1 test and sample entropy measure respectively. Finally, we study the collective behavior of the neurons in terms of two synchronization measures: the cross-correlation coefficient, and the Kuramoto order parameter.

nlin.AO↗

arXiv2024

The bifurcation structure within robust chaos for two-dimensional piecewise-linear maps

We study two-dimensional, two-piece, piecewise-linear maps having two saddle fixed points. Such maps reduce to a four-parameter family and are well known to have a chaotic attractor throughout open regions of parameter space. The purpose of this paper is to determine where and how this attractor undergoes bifurcations. We explore the bifurcation structure numerically by using Eckstein's greatest common divisor algorithm to estimate from sample orbits the number of connected components in the attractor. Where the map is orientation-preserving the numerical results agree with formal results obtained previously through renormalisation. Where the map is orientation-reversing or non-invertible the same renormalisation scheme appears to generate the bifurcation boundaries, but here we need to account for the possibility of some stable low-period solutions. Also the attractor can be destroyed in novel heteroclinic bifurcations (boundary crises) that do not correspond to simple algebraic constraints on the parameters. Overall the results reveal a broadly similar component-doubling bifurcation structure in the orientation-reversing and non-invertible settings, but with some additional complexities.

nlin.CD↗

arXiv2023

On discriminating between Libby-Novick generalized beta and Kumaraswamy distributions: theory and methods

In fitting a continuous bounded data, the generalized beta (and several variants of this distribution) and the two-parameter Kumaraswamy (KW) distributions are the two most prominent univariate continuous distributions that come to our mind. There are some common features between these two rival probability models and to select one of them in a practical situation can be of great interest. Consequently, in this paper, we discuss various methods of selection between the generalized beta proposed by Libby and Novick (1982) (LNGB) and the KW distributions, such as the criteria based on probability of correct selection which is an improvement over the likelihood ratio statistic approach, and also based on pseudo-distance measures. We obtain an approximation for the probability of correct selection under the hypotheses HLNGB and HKW , and select the model that maximizes it. However, our proposal is more appealing in the sense that we provide the comparison study for the LNGB distribution that subsumes both types of classical beta and exponentiated generators (see, for details, Cordeiro et al. 2014; Libby and Novick 1982) which can be a natural competitor of a two-parameter KW distribution in an appropriate scenario.

stat.ME↗

arXiv2023

Robust chaos in orientation-reversing and non-invertible two-dimensional piecewise-linear maps

This paper concerns the two-dimensional border-collision normal form -- a four-parameter family of piecewise-linear maps generalising the Lozi family and relevant to diverse applications. The normal form was recently shown to exhibit a chaotic attractor throughout an open region of parameter space. This was achieved by constructing a trapping region in phase space and an invariant expanding cone in tangent space, but only allowed parameter combinations for which the normal form is invertible and orientation-preserving. This paper generalises the construction to include the non-invertible and orientation-reversing cases. This provides a more complete and unified picture of robust chaos by revealing its presence to be disassociated from the global topological properties of the map. We identify a region of parameter space in which the map exhibits robust chaos, and show that part of the boundary of this region consists of bifurcation points at which the chaotic attractor is destroyed.

nlin.CD↗

arXiv2023

On classical and Bayesian inference for bivariate Poisson conditionals distributions: Theory, methods and applications

Bivariate count data arise in several different disciplines (epidemiology, marketing, sports statistics, etc., to name but a few) and the bivariate Poisson distribution which is a generalization of the Poisson distribution plays an important role in modeling such data. In this article, we consider the inferential aspect of a bivariate Poisson conditionals distribution for which both the conditionals are Poisson but the marginals are typically non-Poisson. It has Poisson marginals only in the case of independence. It appears that a simple iterative procedure under the maximum likelihood method performs quite well as compared with other numerical subroutines, as one would expect in such a case where the MLEs are not available in closed form. In the Bayesian paradigm, both conjugate priors and non-conjugate priors have been utilized and a comparison study has been made via a simulation study. For illustrative purposes, a real-life data set is re-analyzed to exhibit the utility of the proposed two methods of estimation, one under the frequentist approach and the other under the Bayesian paradigm.

stat.ME↗

arXiv2023

Bivariate binomial conditionals distributions with positive and negative correlations: A statistical study

In this article, we discuss a bivariate distribution whose conditionals are univariate binomial distributions and the marginals are not binomial that exhibits negative correlation. Some useful structural properties of this distribution namely marginals, moments, generating functions, stochastic ordering are investigated. Simple proofs of negative correlation, marginal over-dispersion, distribution of sum and conditional given the sum are also derived. The distribution is shown to be a member of the multi-parameter exponential family and some natural but useful consequences are also outlined. The proposed distribution tends to a recently investigated conditional Poisson distribution studied by Ghosh et al. (2020). Finally, the distribution is fitted to two bivariate count data sets with an inherent negative correlation to illustrate its suitability.

stat.ME↗

arXiv2022

On the analysis of a time varying noise-modulated heterogeneous coupled network of Chialvo neurons under the influence of electromagnetic flux

We perform a numerical study on the application of electromagnetic flux on a heterogeneous network of Chialvo neurons represented by a ring-star topology. Heterogeneities are realized by introducing additive noise modulations on both the central-peripheral and the peripheral-peripheral coupling links in the topology that not only vary in space but also in time. The variation in time is understood by two coupling probabilities, one for the central-peripheral connections and the other for the peripheral-peripheral connections respectively, that updates the network topology with each iteration in time. We have further reported the rich spatiotemporal patterns like two-cluster states, chimera states, traveling waves, coherent, and asynchronized states that arise throughout the network dynamics. We have also investigated the appearance of a special kind of asynchronization behavior called "solitary nodes" that have wide range of applications pertaining to real-world nervous systems. In order to characterize the behavior of the nodes under the influence of these heterogeneities, we have studied two different metrics called the "cross-correlation coefficient" and the "synchronization error". Additionally, to capture the statistical property of the network, for example, how complex the system behaves, we have also studied a measure called "sample entropy". Various two-dimensional color-coded plots are presented in the study to exhibit how these metrics/measures behave with the variation of parameters. Finally, how the nodes synchronize or asynchronize is shown via one-dimensional bifurcation diagrams of the last instance of the main dynamical variable, i.e., the state variable associated with the membrane potential, against different network parameters.

math.DS↗

arXiv2022

Numerical bifurcation analysis of improved denatured Morris-Lecar neuron model

It is well-known that the electrical activities of neurons are induced by a wide variety of external factors. This work considers the effect of electromagnetic induction on improved denatured Morris-Lecar neuron model. The dependence of dynamical behaviour of the original denatured Morris-Lecar model on parameters is addressed through numerical bifurcation analysis. This allows us to explore the changes in dynamics of the model qualitatively as parameters are varied. Then we investigate the effects of external periodic current and electromagnetic flux on the dynamical properties of the improved denatured Morris-Lecar neuron model. Different types of dynamical behaviour, ranging from regular periodic spiking to complex bursting, are found when the multiple parameters are varied simultaneously. The improved model could be applied to research where simple models are required for physiological and pathophysiological responses in neurons.

math.DS↗