arXiv subjects

R. K. Brojen Singh

Publications and source records attributed to R. K. Brojen Singh.

At least 19 recordsLinked to original sources

arXiv2026

A hybrid dynamical-stochastic model of maximum temperature time series of Imphal, Northeast India incorporating nonlinear feedback and noise diagnostics

Climate variability is a complex phenomenon resulting from numerous interacting components of a climate system across a wide range of temporal and spatial scales. Although significant advances have been made in understanding global climate variability, there are relatively less studies on regional climate modeling, particularly in developing countries. In this work, we propose a framework of data driven hybrid dynamical stochastic modeling to investigate the variability of maximum temperature recorded for the capital city of Imphal in the state of Manipur, located in the Northeast India. In light of increasing concerns over global warming, studying maximum temperature variability over varying time scales is an important area of research. Analysis using publicly available climate data over the course of 73 years, our approach yields key insights into the temperature dynamics, such as a positive increase in temperature in the region during the period investigated. Our hybrid model, combining spectral analysis and Fourier decomposition methods with stochastic noise terms and nonlinear feedback mechanisms, is found to effectively reproduce the observed dynamics of maximum temperature variability with high accuracy. Our results are validated by robust statistical and qualitative tests. We further derive Langevin and Fokker-Planck equations for the maximum temperature dynamics, offering the theoretical ground and analytical interpretation of the model that links the temperature dynamics with underlying physical principles.

nlin.CD↗

arXiv2026

Chaotic Dynamics and Bifurcation Analysis of the Hindmarsh-Rose Neuron Model with Blue-Sky Catastrophe under Magnetic Field Influence

We investigate the impact of magnetic-field-induced feedback on the dynamics of a Hindmarsh-Rose neuron model exhibiting a blue-sky catastrophe. By introducing a magnetic flux variable that couples nonlinearly to the membrane potential, we demonstrate that electromagnetic effects profoundly reshape neuronal firing patterns and bifurcation structure. Interspike-interval bifurcation analysis reveals a nonmonotonic dependence on the magnetic coupling strength, with weak coupling preserving regular spiking and bursting, intermediate coupling promoting chaotic bursting, and strong coupling yielding structured irregular dynamics. These transitions are quantitatively characterized using the largest Lyapunov exponent computed via the Wolf algorithm and supported by Poincaré sections and time-series analysis. Our results establish electromagnetic feedback as a robust and tunable mechanism for controlling instability and chaos in slow-fast neuronal systems.

physics.comp-ph↗

arXiv2025

On study of cell proliferation and diffusion using nonlinear transforms of heat equation solutions

Cell proliferation and diffusion can be modeled through reaction-diffusion systems describing the space-time evolution of a density variable. In this work, we present non-linear transformations of heat equation solutions to model cellular growth and diffusion using a Richards growth function. The solutions are obtained by using two-variable Hermite Polynomials. We estimated the parameters of the Richards function by comparing the model solutions with the experimentally observed data from scratch assays. To check robustness of the parameters estimated, we used a fractional Brownian Motion (fBM) field type noise with given Hurst exponent (H) for minimizing residual errors. We found that the parameters can be robustly estimated and match with previous estimations. Further, we also confirmed that the spatial-temporal patterns of cell density in the experiments can be well described by the solutions developed using the proposed nonlinear transforms method.

nlin.CD↗

arXiv2025

On Optimal Control of a Genotype-Structured Prey-Predator System for Ecological Rescue and Oscillation Restoration

Evolutionary changes impacts interactions among populations and can disrupt ecosystems by driving extinctions or by collapsing population oscillations, posing significant challenges to biodiversity conservation. This study addresses the ecological rescue of a predator population threatened by a mutant prey population using optimal control method. To study this, we proposed a model which incorporates genotypically structured prey comprising of wild-type, heterozygous and mutant prey types and predator population. We proved that this model has both local and global existence and uniqueness of solutions ensuring the model robustness. Then, we applied optimal control method along with Pontryagin Maximum Principle by incorporating a control input in the model to minimize the mutant population and subsequently to stabilize the ecosystem. The numerical results clearly reveal that the undesired dynamics of the model can be controlled showing the suppression of the mutant, rescues the predator, and restores the oscillatory dynamics of the system. These findings demonstrate the efficacy of the control strategy and provide a mathematical framework for managing such ecological disruptions

nlin.CD↗

arXiv2025

Lower bound of entropy production at short time scales for noise-driven stochastic systems

The second law of thermodynamics governs that nonequilibrium systems evolve towards states of higher entropy over time. However, it does not specify the rate of this evolution and the role of fluctuations that impact the system's dynamics. Entropy production quantifies how far a system is driven away from equilibrium and provides a measure of irreversibility. In stochastic systems, entropy production becomes essential for understanding the approach to nonequilibrium states. While macroscopic observations provide valuable insights, they often overlook the local behaviors of the system, governed by fluctuations. In this study, we focus on measuring the lower bound of entropy production at short time scales for generalized stochastic systems by calculating the Kullback-Leibler divergence (KLD) between the probability density functions of forward and backward trajectories. By analysing the entropy production across sliding time scales, we uncover patterns that reveal distinctions between local, small-scale dynamics and the global, macroscopic behavior, offering deeper insights into the system's departure from equilibrium. We also analysed the effects of switching to different types of noise or fluctuations and found that the observations at larger time scales provide no distinction between the different forms of noise while at short time scales, the distinction is significant.

cond-mat.stat-mech↗

arXiv2024

On study of transition fronts of Fisher-KPP type reaction-diffusion PDEs by non-linear transformations into exactly solvable class

Spatio-temporal dynamics of the evolution of population involving growth and diffusion processes can be modeled by class of partial diffusion equations (PDEs) known as reaction-diffusion systems. In this work, we developed a nonlinear transformations method that converts the original nonlinear Fisher-KPP class of PDEs into an exactly solvable class. We then demonstrated that the proposed nonlinear transformation method intrinsically preserves the relaxation behavior of the solutions to asymptotic values of the non-linear dynamical system. We also show that these particular transforms are very amenable to yield an exact closed form solution in terms of the heat kernel and analytical approximations through the two variable Hermite polynomials. With this proposed method, we calculated the front velocity and shape of the propagating wave and showed how the non-linear transformation affects these parameters for both short and long epochs. As applications, we focus on solving pertinent cases of the Fisher-KPP type of PDEs relating to the evolutionary dynamics by assigning fitness to the mutant gene according to zygosity conditions. We calculated the relaxation of velocity with the parameters of the initial conditions in the following cases, namely, the Fisher, the heterozygote inferior fitness, the heterozygote superior fitness, and finally a general nonlinearity case. We also verified previous conjectures through the exact solutions computed using the proposed method.

q-bio.PE↗

arXiv2024

Pre-oligomerisation stochastic dynamics of prions driven by water molecules

Prions are proteinaceous infectious particles that cause neurodegenerative diseases in humans and animals. The complex nature of prions, with respect to their conformations and aggregations, has been an important area of research for quite some time. Here, we develop a model of prion dynamics prior to the formation of oligomers and subsequent development of prion diseases within a stochastic framework, based on the analytical Master Equation and Stochastic Simulation Algorithm by Gillespie. The results that we obtain shows that solvent water molecules act as driving agents in the dynamics of prion aggregation. Further, it is found that aggregated and non-aggregated proteins tend to co-exist in an equilibrium state, depending upon the reaction rate constants. These results may provide a theoretical and qualitative contexts of possible therapeutic strategies in the treatment of prion diseases.

physics.bio-ph↗

arXiv2024

Exploring the Interplay of Intrinsic Fluctuation and Complexity in Intracellular Calcium Dynamics

The concentration of intracellular calcium ion (Ca$^{2+}$) exhibits complex oscillations, including bursting and chaos, as observed experimentally. These dynamics are influenced by inherent fluctuations within cells, which serve as crucial determinants in cellular decision-making processes and fate determination. In this study, we systematically explore the interplay between intrinsic fluctuation and the complexity of intracellular cytosolic Ca$^{2+}$ dynamics using complexity measures such as permutation entropy (PE) and statistical complexity (SC). Using the chemical Langevin equation, we simulate the stochastic dynamics of cytosolic Ca$^{2+}$. Our findings reveal that PE and SC effectively characterize the diverse, dynamic states of cytosolic Ca$^{2+}$ and illustrate their interactions with intrinsic fluctuation. PE analysis elucidates that the chaotic state is more sensitive to intrinsic fluctuation than the other periodic states. Furthermore, we identify distinct states of cytosolic Ca$^{2+}$ occupying specific locations within the theoretical bounds of the complexity-entropy causality plane. These locations indicate varying complexity and information content as intrinsic fluctuation varies. When adjusting the permutation order, the SC for the different states exhibits peaks in an intermediate range of intrinsic fluctuation values. Additionally, we identify scale-free or self-similar patterns in this intermediate range, which are further corroborated by multifractal detrended fluctuation analysis. These high-complexity states likely correspond to optimal Ca$^{2+}$ dynamics with biological significance, revealing rich and complex dynamics shaped by the interplay of intrinsic fluctuation and complexity. Our investigation enhances our understanding of how intrinsic fluctuation modulates the complexity of intracellular Ca$^{2+}$ dynamics that play crucial roles in biological cells.

nlin.AO↗

arXiv2024

Quantifying dissipation in stochastic complex oscillations

Fluctuations-driven complex oscillations are experimentally observed in cellular systems such as hepatocytes, cardiac cells, neuronal cells, etc. These systems are generally operating in regimes far from thermodynamic equilibrium. To study nonequilibrium thermodynamic properties such as energy dissipation in stochastic complex oscillations, we consider stochastic modeling of two nonlinear biological oscillators, namely, the intracellular calcium (Ca$^{2+}$) oscillation model and the Hindmarsh-Rose model for neuronal dynamics. These models exhibit various types of complex oscillations like bursting and quasi-periodic oscillations for various system parameter values. In this work, we formulate open chemical reaction schemes for the two model systems driving the systems far from thermodynamic equilibrium. We then analyze the steady-state total entropy production rate (EPR) in the various types of stochastic complex oscillations. Our results show higher values of steady-state total EPR in stochastic complex oscillations than simple periodic oscillations. Moreover, in the Hindmarsh-Rose neuronal model, we observe an order-to-disorder transition from periodic (organized) bursts of spikes to chaotic (unorganized) oscillations with distinct behaviors of steady-state total EPR. Our results reveal that stochastic complex oscillations are produced at the cost of higher energy consumption and that it requires a higher thermodynamic cost to maintain the periodic bursts than chaotic oscillations. Our findings indicate that complex cellular regulatory or signaling processes by Ca$^{2+}$ that help perform complex tasks of the nervous system or rich information coding by neurons involve a higher thermodynamic cost. The results deepen our understanding of energy dissipation in nonlinear, nonequilibrium biological systems with stochastic complex oscillatory dynamics.

physics.chem-ph↗

arXiv2024

Analysis of the structural complexity of Crab Nebula observed at radio frequency using a multifractal approach

The Crab Nebula is an astrophysical system that exhibits complex morphological patterns at different observing frequencies. We carry out a systematic investigation of the structural complexity of the nebula using publicly available imaging data at radio frequency. For the analysis, we use the well-known multifractal detrended fluctuation analysis in two dimensions. We find that radio data exhibit long-range correlations, as expected from the underlying physics of the supernova explosion and evolution. The correlations follow a power-law scaling with length scales. The structural complexity is found to be multifractal in nature, as evidenced by the dependence of the generalized Hurst exponent on the order of the moments of the detrended fluctuation function. By repeating the analysis on shuffled data, we further probe the origin of the multifractality in the radio imaging data. For the radio data, we find that the probability density function is close to a Gaussian form. Hence, the multifractal behavior is due to the differing nature of long-range correlations of the large and small detrended fluctuation field values. We investigate the multifractal parameters across different partitions of the radio image and find that the structures across the image are highly heterogeneous, making the Crab Nebula a structurally complex astrophysical system. Our analysis thus provides a fresh perspective on the morphology of the Crab Nebula from a complexity science viewpoint.

nlin.AO↗

arXiv2023

Network based control strategies for sustainable management of Lantana camara

Control studies in ecological models of networks involving invasive plants can offer tangible management strategies. Framing control policies to tackle problems posed by invasive plants on indigenous plant diversity under the sustainable developmental goals framework is the main motivation of this paper. Based on the reported experimental and theoretical observations, we propose minimal ecological models of direct interactions of \textit{Lantana camara} with other entitites e.g. other indigenous plants (denoted by Control-plant) and soil microbes. The species' abundance variables represented by the nodes in the model networks follow generalized Lotka-Volterra dynamics and input signals are incorporated at appropriate driver nodes to control the \textit{Lantana camara} outgrowth. Analysis with Lie algebra and controllability criteria showed that our model systems are controllable with minimum of two control input signals. Analytical results of our model equations indicated that successive interventions are required to increase the abundance of control-plant, the microbes and suppress \textit{Lantana camara}. We observed from the numerical analysis with LQR algorithm that the number of interventions to be taken to control the \textit{Lantana camara} outgrowth depends on the choice of various important parameters such as intervention time, effort and penalty etc. Further, the increase in nonlinear terms contributed from self-loops in the network model shows the persistence of \textit{L. camara} and how it drives the coexistence of the species. We propose that parameters we have identified in our study needed to be considered and analyzed extensively for designing sustainable policies to control invasive species in an ecosystem.

nlin.AO↗

arXiv2022

Stochastic approach to study the properties of the complex patterns observed in cytokine and T-cells interaction process

Patterns in complex systems store hidden information of the system which is needed to be explored. We present a simple model of cytokine and T-cells interaction and studied the model within stochastic framework by constructing Master equation of the system and solving it. The solved probability distribution function of the model show classical Poisson pattern in the large population limit $M,Z\rightarrow large$ indicating the system has the tendency to attract a large number small-scale random processes of the cytokine population towards the basin of attraction of the system by segregating from nonrandom processes. Further, in the large $\langle Z\rangle$ limit, the pattern transform to classical Normal pattern, where, uncorrelated small-scale fluctuations are wiped out to form a regular but memoryless spatiotemporal aggregated pattern. The estimated noise using Fano factor shows clearly that the cytokine dynamics is noise induced process driving the system far away from equilibrium.

q-bio.PE↗

arXiv2022

Spatiotemporal patterns of Covid-19 pandemic in India: Inferences of pandemic dynamics from data analysis

Modeling and analysis of the large scale Covid-19 pandemic data can yield inferences about it's dynamics and characteristics of disease propagation. These inferences can then be correlated with contextual factors like population density, effects of strategic interventions, heterogeneous disease propagation etc, and such set of validated inferences can serve as precedents for designing of subsequent mitigation strategies. In this work, we present the analysis of Covid-19 pandemic data in Indian context using growth functions fitting procedure and harmonic analysis method. Our results of growth function fitting to the data indicate that the growth function parameters are quite sensitive to the growth of the infected population indicating positive impact of lockdown strategy, identification of inflection point and nearly synchronous statistical features of disease spreading. The harmonic analysis of the data shows the countrywide synchronous incident features due to simultaneous implementation of control strategies. However, if one analyzes the data from each state of the India, one can see various forms of travelling waves in the countrywide wave pattern. Hence, one needs to do these analysis from time to time to understand the effectiveness of any control strategy and to closely look at the disease propagation to devise the required type of mitigation strategies.

q-bio.PE↗

arXiv2022

Thermodynamic Uncertainty Relation in the interlinked cascade of RabGTPases

We model the well-known interlinked cascade of Rab GTPases found in eukaryotic cells by using a network of Markov states to investigate the universal Thermodynamic Uncertainty Relation for the non-equilibrium system. First, we prove numerically the TUR in both single Rab species model and the interlinked two Rab species model. Our results show that when two Rab GTPase proteins are interlinked at far from equilibrium, the thermodynamic cost and hence precision is greatly enhanced as compared to single species switching. This implies that at far from equilibrium, the proteins tries to optimise the precision of the performance of their biomolecular processes by forming interlinks in the cascade. Again,our results imply that the interlinked cascade (or oscillator) can achieve a range of tunable rate constants (or frequencies) which suggests a means of maintaining its robustness. Lastly, we highlight a close relation between thermodynamic cost-precision, triangular motifs and disease dynamics.

physics.bio-ph↗

arXiv2022

Evolution of language driven by social dynamics

The survival of endangered languages in complex language competition depends on socio-cultural status and honour endowed (by itself and by the other) among them. The restriction in the endorsement of this honour leads to language extinction of one language, and rise of the other. Endorsing proper mutual honour each other trigger the co-existence of language speakers and can save both languages from extinction. The lost of respect to each other drives the death of both languages. We found a minimal or critical mutual honour (a=0.9635) which protects the two languages from extinction. The increase in mutual honour from this minimal value allows increase in the populations of the two languages speakers. The state of co-existence of competing languages abolishes the concept of minority and majority in language competition which can be obtained by mutual honour. Further, excess biased honour to a particular language (minority or majority) force the language to extinct. In mean-field approximation of language competition, magnetization parameter can be taken as an indicator of survival of a language.

physics.soc-ph↗

arXiv2021

Dynamics of unfolded protein aggregation

Unfolded protein aggregation in cellular system is a problem causing various types of diseases depending on which type unfolded proteins aggregate. This phenomenon of aggregation may take place during production, storage, shipment or delivery in the cellular medium. In the present work, we studied a simplified and extended version of unfolded protein aggregation model by Lumry and Eyring using stochastic approach. We solved analytically the Master equation of the model for the probability distribution $P(x,t)$ of the unfolded protein population and the solution was found to be time dependent complex binomial distribution. In the large population limit $P(x,t)\sim Λ(x,t)\times Pois(x,t)$. Further, the distribution became Normal distribution at large population and mean of the distribution limit: $P(x,t)\simΛ(x,t)\times N(\langle qx\rangle,\langle qx\rangle)$. The fluctuations inherent in the dynamics measured by Fano factor can have sub-Poisson, Poisson and super-Poisson at different situations.

q-bio.SC↗

arXiv2021

Epidemiological parameter sensitivity in Covid-19 dynamics and estimation

Covid-19 is one of the most dreaded pandemics/epidemics in the world threatening the human population. The dynamics of this pandemic is quite complicated and prediction of pandemic states often fails. In this work, we study and correlate the SIR epidemiological model with the ongoing pandemic and found that pandemic dynamics and states are quite sensitively dependent on model parameters. The analysis of the exact parametric solution of the deterministic SIR model shows that the fixed points ($g^*$) depend on the SIR parameters, where, if $g^*\langle\fracγ{βx_0}$ then $g^*$ is stable and the pandemic can be controlled, whereas, if $g^*\rangle\fracγ{βx_0}$ then $g^*$ is unstable indicating active pandemic state, and $g^*=0$ corresponds to an endemic state. The dynamics show asymptotic stability bifurcation. The analytical solution of the stochastic SIR model allows to predict endemic time $t_E\propto\frac{1}γ$ and mean infected population becomes constant for small values of $γ$. The noise in the system even can modulate pandemic dynamics. Hence, we estimated the values of these parameters during lockdown periods using the ABC SSA algorithm and found strong dependence on control strategy, namely, lockdown and follows power-law behaviors. The numerical results show strong agreement with the real data and have the positive effect of social distancing or lockdown in the pandemic control.

q-bio.PE↗

arXiv2021

Functional switching among dynamic neuronal hub-nodes in the brain induces transition of cognitive states

The cognitive states have broadly been divided into waking, rapid eye movement sleep and non-REMS. Although the mechanism of state transition is unknown, it has been proposed that functional activation/deactivation among different brain regions leads to such transition. As analysis of electroencephalogram allows us exploring properties and association among brain regions, we exploited it to address our query. We have recorded the frontal and occipital cortical EEG from surgically prepared chronic freely moving, normally behaving rats and classified their vigilance states and vigilance state-transitions. The complexity analysis carried out by computing multifractal spectrum width categorized VST as highly non-linear and complex than their participating vigilance states. The EEG signals were decomposed into frequency ranges as that of classical human Delta, Theta, Alpha, Beta and Gamma oscillations. The dynamic network attributes of these oscillations has shown compelling topological correlation between the frontal and occipital regions of the brain during conscious states. The topological trends of the underlying hierarchical network organization have been characterized by the percentage of the hub and non-hub nodes, that further determines the global and local connectivity trends. This has revealed interesting insights of functional disconnection during NREMS due to decrease in their number of hub-nodes as compared to waking state. There is also switching behaviour in the ratio of hub/non-hub nodes between frontal and occipital region during NREMS-Wake and Wake-NREMS transitions. Our findings provide support as proof-of-principle of functional regional inactivation or activation of hub-nodes as the gradual switching mechanism towards transitioning of cognitive states in a graded manner, wake to sleep or vice versa; the detailed neuro-physio-chemical mechanism needs further study.

q-bio.NC↗