arXiv subjects

Chittaranjan Hens

Publications and source records attributed to Chittaranjan Hens.

At least 55 records · Page 3Linked to original sources

arXiv2022

Controlling species densities in structurally perturbed intransitive cycles with higher-order interactions

The persistence of biodiversity of species is a challenging proposition in ecological communities in the face of Darwinian selection. The present article investigates beyond the pairwise competitive interactions and provides a novel perspective for understanding the influence of higher-order interactions on the evolution of social phenotypes. Our simple model yields a prosperous outlook to demonstrate the impact of perturbations on intransitive competitive higher-order interactions. Using a mathematical technique, we show how alone the perturbed interaction network can quickly determine the coexistence equilibrium of competing species instead of solving a large system of ordinary differential equations. It is possible to split the system into multiple feasible cluster states depending on the number of perturbations. Our analysis also reveals the ratio between the unperturbed and perturbed species is inversely proportional to the amount of employed perturbation. Our results suggest that nonlinear dynamical systems and interaction topologies can be interplayed to comprehend species' coexistence under adverse conditions. Particularly our findings signify that less competition between two species increases their abundance and outperforms others.

q-bio.PE↗

arXiv2022

Resetting mediated navigation of active Brownian searcher in a homogeneous topography

Designing navigation strategies for search time optimization remains of interest in various interdisciplinary branches in science. In here, we focus on microscopic self-propelled searchers namely active Brownian walkers in noisy and confined environment which are mediated by one such autonomous strategy namely resetting. As such, resetting stops the motion and compels the walkers to restart from the initial configuration intermittently according to an external timer that does not require control by the walkers. In particular, the resetting coordinates are either quenched (fixed) or annealed (fluctuating) over the entire topography. Although the strategy relies upon simple rules, it shows a significant ramification on the search time statistics in contrast to the original search. We show that the resetting driven protocols mitigate the performance of these active searchers based, robustly, on the inherent search time fluctuations. Notably, for the annealed condition, resetting is always found to expedite the search process. These features, as well as their applicability to more general optimization problems starting from queuing systems, computer science to living systems, make resetting based strategies universally promising.

cond-mat.soft↗

arXiv2022

Model-free prediction of multistability using echo state network

In the field of complex dynamics, multistable attractors have been gaining a significant attention due to its unpredictability in occurrence and extreme sensitivity to initial conditions. Co-existing attractors are abundant in diverse systems ranging from climate to finance, ecological to social systems. In this article, we investigate a data-driven approach to infer different dynamics of a multistable system using echo state network (ESN). We start with a parameter-aware reservoir and predict diverse dynamics for different parameter values. Interestingly, machine is able to reproduce the dynamics almost perfectly even at distant parameters which lie considerably far from the parameter values related to the training dynamics. In continuation, we can predict whole bifurcation diagram significant accuracy as well. We extend this study for exploring various dynamics of multistable attractors at unknown parameter value. While, we train the machine with the dynamics of only one attarctor at parameter $p$, it can capture the dynamics of co-existing attractor at a new parameter value $p+Δp$. Continuing the simulation for multiple set of initial conditions, we can identify the basins for different attractors. We generalize the results by applying the scheme on two distinct multistable systems.

nlin.AO↗

arXiv2022

Topological synchronization of chaotic systems

A chaotic dynamics is typically characterized by the emergence of strange attractors with their fractal or multifractal structure. On the other hand, chaotic synchronization is a unique emergent self-organization phenomenon in nature. Classically, synchronization was characterized in terms of macroscopic parameters, such as the spectrum of Lyapunov exponents. Recently, however, we attempted a microscopic description of synchronization, called topological synchronization, and showed that chaotic synchronization is, in fact, a continuous process that starts in low-density areas of the attractor. Here we analyze the relation between the two emergent phenomena by shifting the descriptive level of topological synchronization to account for the multifractal nature of the visited attractors. Namely, we measure the generalized dimension of the system and monitor how it changes while increasing the coupling strength. We show that during the gradual process of topological adjustment in phase space, the multifractal structures of each strange attractor of the two coupled oscillators continuously converge, taking a similar form, until complete topological synchronization ensues. According to our results, chaotic synchronization has a specific trait in various systems, from continuous systems and discrete maps to high dimensional systems: synchronization initiates from the sparse areas of the attractor, and it creates what we termed as the zipper effect, a distinctive pattern in the multifractal structure of the system that reveals the microscopic buildup of the synchronization process. Topological synchronization offers, therefore, a more detailed microscopic description of chaotic synchronization and reveals new information about the process even in cases of high mismatch parameters.

nlin.CD↗

arXiv2022

Effect of mobility in the rock-paper-scissor dynamics with high mortality

In the evolutionary dynamics of a rock-paper-scissor (RPS) model, the effect of natural death plays a major role in determining the fate of the system. Coexistence, being an unstable fixed point of the model becomes very sensitive towards this parameter. In order to study the effect of mobility in such a system which has explicit dependence on mortality, we perform Monte Carlo simulation on a $2$-dimensional lattice having three cyclically-competing species. The spatio-temporal dynamics has been studied along with the two-site correlation function. Spatial distribution exhibits emergence of spiral patterns in the presence of diffusion. It reveals that the joint effect of death rate and diffusion (migration) leads to new coexistence and extinction scenarios.

cond-mat.stat-mech↗

arXiv2021

Role of assortativity in predicting burst synchronization using echo state network

In this study, we use a reservoir computing based echo state network (ESN) to predict the collective burst synchronization of neurons. Specifically, we investigate the ability of ESN in predicting the burst synchronization of an ensemble of Rulkov neurons placed on a scale-free network. We have shown that a limited number of nodal dynamics used as input in the machine can capture the real trend of burst synchronization in this network. Further, we investigate on the proper selection of nodal inputs of degree-degree (positive and negative) correlated networks. We show that for a disassortative network, selection of different input nodes based on degree has no significant role in machine's prediction. However, in the case of assortative network, training the machine with the information (i.e time series) of low-degree nodes gives better results in predicting the burst synchronization. Finally, we explain the underlying mechanism responsible for observing this differences in prediction in a degree correlated network.

q-bio.NC↗

arXiv2021

Spatiotemporal instabilities and pattern formation in systems of diffusively coupled Izhikevich neurons

Neurons are often connected, spatially and temporally, in phenomenal ways that promote wave propagation. Therefore, it is essential to analyze the emergent spatiotemporal patterns to understand the working mechanism of brain activity, especially in cortical areas. Here, we present an explicit mathematical analysis, corroborated by numerical results, to identify and investigate the spatiotemporal, non-uniform, patterns that emerge due to instability in an extended homogeneous 2D spatial domain, using the excitable Izhikevich neuron model. We examine diffusive instability and perform bifurcation and fixed-point analyses to characterize the patterns and their stability. Then, we derive analytically the amplitude equations that establish the activities of reaction-diffusion structures. We report on the emergence of diverse spatial structures including hexagonal and mixed-type patterns by providing a systematic mathematical approach, including variations in correlated oscillations, pattern variations and amplitude fluctuations. Our work shows that the emergence of spatiotemporal behavior, commonly found in excitable systems, has the potential to contribute significantly to the study of diffusively-coupled biophysical systems at large.

nlin.PS↗

arXiv2021

Identifying symmetries and predicting cluster synchronization in complex networks

Symmetries in a network connectivity regulate how the graph's functioning organizes into clustered states. Classical methods for tracing the symmetry group of a network require very high computational costs, and therefore they are of hard, or even impossible, execution for large sized graphs. We here unveil that there is a direct connection between the elements of the eigen-vector centrality and the clusters of a network. This gives a fresh framework for cluster analysis in undirected and connected graphs, whose computational cost is linear in $N$. We show that the cluster identification is in perfect agreement with symmetry based analyses, and it allows predicting the sequence of synchronized clusters which form before the eventual occurrence of global synchronization.

nlin.AO↗

arXiv2021

Amplification of explosive width in complex networks

We present an adaptive coupling strategy to induce hysteresis/explosive synchronization (ES) in complex networks of phase oscillators Sakaguchi-Kuramoto model). The coupling strategy ensures explosive synchronization with significant explosive width enhancement. Results show the robustness of the strategy and the strategy can diminish (by inducing enhanced hysteresis loop) the contrarian impact of phase frustration in the network, irrespective of network structure or frequency distributions. Additionally, we design a set of frequency for the oscillators which eventually ensure complete in-phase synchronization behavior among these oscillators (with enhanced explosive width) in the case of adaptive-coupling scheme. Based on a mean-field analysis, we develop a semi-analytical formalism, which can accurately predict the backward transition of synchronization order parameter.

nlin.AO↗

arXiv2020

Infection spreading and recovery in a square lattice

We investigate spreading and recovery of disease in a square lattice, and in particular, emphasize the role of the initial distribution of infected patches in the network, on the progression of an endemic and initiation of a recovery process, if any, due to migration of both the susceptible and infected hosts. The disease starts in the lattice with three possible initial distribution patterns of infected and infection-free sites, infected core patches (ICP), infected peripheral patches (IPP) and randomly distributed infected patches (RDIP). Our results show that infection spreads monotonically in the lattice with increasing migration without showing any sign of recovery in the ICP case. In the IPP case, it follows a similar monotonic progression with increasing migration, however, a self-organized healing process starts for higher migration, leading the lattice to full recovery at a critical rate of migration. Encouragingly, for the initial RDIP arrangement, chances of recovery are much higher with a lower rate of critical migration. An eigenvalue based semi-analytical study is made to determine the critical migration rate for realizing a stable infection-free lattice. The initial fraction of infected patches and the force of infection play significant roles in the self-organized recovery. They follow an exponential law, for the RDIP case, that governs the recovery process. For the frustrating case of ICP arrangement, we propose a random rewiring of links in the lattice allowing long-distance migratory paths that effectively initiate a recovery process. Global prevalence of infection thereby declines and progressively improves with the rewiring probability that follows a power law with the critical migration and leads to the birth of emergent infection-free networks.

q-bio.PE↗

arXiv2020

Optimal test-kit based intervention strategy of epidemic spreading in heterogeneous complex networks

We propose a deterministic compartmental model of infectious disease which considers the test-kits as an important ingredient for the suppression and mitigation of epidemics. A rigorous simulation (with analytical argument) is provided to reveal the effective reduction of final outbreak size and peak of infection as a function of basic reproduction number in a single patch. Further, to study the impact of long and short-distance human migration among the patches, we have considered heterogeneous networks where the linear diffusive connectivity is determined by the network link structure. We numerically confirm that implementation of test-kits in the fraction of nodes (patches) having larger degrees or betweenness centralities can reduce the peak of infection (as well as final outbreak size) significantly. A next-generation matrix based analytical treatment is provided to find out the critical transmission probability in the entire network for the onset of epidemics. Finally, the optimal intervention strategy is validated in two real networks: global airport networks and transportation networks of Kolkata, India.

physics.soc-ph↗

arXiv2020

Mitigating long transient time in deterministic systems by resetting

How long does a trajectory take to reach a stable equilibrium point in the basin of attraction of a dynamical system? This is a question of quite general interest, and has stimulated a lot of activities in dynamical and stochastic systems where the metric of this estimation is often known as the transient or first passage time. In nonlinear systems, one often experiences long transients due to their underlying dynamics. We apply resetting or restart, an emerging concept in statistical physics and stochastic process, to mitigate the detrimental effects of prolonged transients in deterministic dynamical systems. We show that stopping an ongoing process at intermittent time only to restart all over from a spatial control line, can dramatically expedite its completion, resulting in a huge decrease in mean transient time. Moreover, our study unfolds a net reduction in fluctuations around the mean. Our claim is established with detailed numerical studies on the Stuart-Landau limit cycle oscillator and chaotic Lorenz system under different resetting strategies. Our analysis opens up a door to control the mean and fluctuations in transient time by unifying the original dynamics with an external stochastic or periodic timer, and poses open questions on the optimal way to harness transients in dynamical systems.

nlin.AO↗

arXiv2020

Response times of nodes in a complex network environment -- two potential derivation tracks

The spread of perturbative signals in complex networks is governed by the combined effect of the network topology and its intrinsic nonlinear dynamics. Recently, the resulting spreading patterns have been analyzed and predicted, shown to depend on a single scaling relationship, linking a node's weighted degree $S_i$ to its intrinsic response time $τ_i$. The relevant scaling exponent $θ$ can be analytically traced to the system's nonlinear dynamics. Here we show that $θ$ can be obtained via two different derivation tracks, leading to seemingly different functions. Analyzing the resulting predictions, we find that, despite their distinct form, they are fully consistent, predicting the exact same scaling relationship under potentially diverse types of dynamics.

nlin.AO↗

arXiv2020

Routes to extreme events in dynamical systems: Dynamical and Statistical Characteristics

Intermittent large amplitude events are seen in the temporal evolution of a state variable of many dynamical systems. Such intermittent large events suddenly start appearing in dynamical systems at a critical value of a system parameter and continues for a range of parameter values. Three important processes of instabilities, namely, interior crisis, Pomeau-Manneville intermittency and the breakdown of quasiperiodic motion, are most common as observed in many systems that lead to such occasional and rare transitions to large amplitude spiking events. We characterize these occasional large events as extreme events if they are larger than a statistically defined significant height. We present two exemplary systems, a single system and a coupled system to illustrate how the instabilities work to originate as extreme events and they manifest as non-trivial dynamical events. We illustrate the dynamical and statistical properties of such events.

nlin.CD↗

arXiv2020

Mortality makes coexistence vulnerable in evolutionary game of rock-paper-scissors

Multiple species in the ecosystem are believed to compete cyclically for survival and thus maintain balance in nature. Stochasticity has also an inevitable role in this dynamics. Considering these attributes of nature, the stochastic dynamics of the rock-paper-scissor model based on the idea of cyclic dominance becomes an effective tool to capture different aspects of ecosystem. The evolutionary dynamics of this model crucially depends on different interactions representing different natural habits. In this framework we explore the role of mortality of individual organism in the collective survival of a species. For this purpose a new parameter called `natural death' is introduced. It is meant for bringing about the decease of an individual irrespective of any intra- and interspecific interaction. We perform Monte Carlo simulation followed by the stability analysis of different fixed points of defined rate equations and observe that the natural death rate is surprisingly one of the most significant factors in deciding whether an ecosystem would come up with a coexistence or a single species survival.

q-bio.PE↗

arXiv2020

Emergence of mixed mode oscillations in random networks of diverse excitable neurons: the role of neighbors and electrical coupling

In this paper, we focus on the emergence of diverse neuronal oscillations arising in a mixed population of neurons with different excitability properties. These properties produce mixed mode oscillations (MMOs) characterized by the combination of large amplitudes and alternate subthreshold or small amplitude oscillations. Considering the biophysically plausible, Izhikevich neuron model, we demonstrate that various MMOs, including MMBOs (mixed mode bursting oscillations) and synchronized tonic spiking appear in a randomly connected network of neurons, where a fraction of them is in a quiescent (silent) state and the rest in self-oscillatory (firing) states. We show that MMOs and other patterns of neural activity depend on the number of oscillatory neighbors of quiescent nodes and on electrical coupling strengths. Our results are verified by constructing a reduced-order network model and supported by systematic bifurcation diagrams as well as for a small-world network. Our results suggest that, for weak couplings, MMOs appear due to the de-synchronization of a large number of quiescent neurons in the networks. The quiescent neurons together with the firing neurons produce high frequency oscillations and bursting activity. The overarching goal is to uncover a favorable network architecture and suitable parameter spaces where Izhikevich model neurons generate diverse responses ranging from MMOs to tonic spiking.

nlin.AO↗

arXiv2020

Effect of repulsive links on frustration in attractively coupled networks

We investigate the impact of attractive-repulsive interaction in networks of limit-cycle oscillators. Mainly we focus on the design principle for generating an anti-phase state between adjacent nodes in a complex network. We establish that a partial negative control throughout the branches of a spanning tree inside the positively coupled limit-cycle oscillators works efficiently well in comparison with randomly chosen negative links to establish zero frustration (anti-phase synchronization) in bipartite graphs. Based on the emergence of zero frustration, we develop a universal 0-$π$ rule to understand the anti-phase synchronization in a bipartite graph. Further, this rule is used to construct a non-bipartite graph for a given non-zero frustrated value. We finally show the generality of 0-$π$ rule by implementing it in arbitrary undirected non-bipartite graphs of attractive-repulsively coupled limit-cycle oscillators and successfully calculate the non-zero frustration value which matches with numerical data. The validation of the rule is checked through the bifurcation analysis of small networks. Our work may unveil the underlying mechanism of several synchronization phenomena that exist in a network of oscillators having a mixed type of coupling.

nlin.AO↗

arXiv2019

Optimizing synchronization in multiplex networks of phase oscillators

We present an analytical scheme to achieve optimal synchronization in multiplex networks of frustrated and non-frustrated phase oscillators. We derive a multiplex synchrony alignment function (MSAF) for that purpose, the expression of which consists of structural as well as dynamical information of the layers of the multiplex network. Analyzing the MSAF, a set of frequencies (optimal frequencies) is determined to achieve optimal synchronization in the network. Further, using the scheme, we show that perfect synchronization can be achieved in a layer of the multiplex network for given coupling strength and phase frustration parameters. The analytical scheme presented here has been tested for heterogeneous multiplex networks of frustrated and non-frustrated Kuramoto dynamics.

nlin.AO↗