Exotic swarming dynamics of high-dimensional swarmalators.

Swarmalators are oscillators that can swarm as well as sync via a dynamic balance between their spatial proximity and phase similarity. Swarmalator models employed so far in the literature comprise only one-dimensional phase variables to represent the intrinsic dynamics of the natural collectives. Nevertheless, the latter can indeed be represented more realistically by high-dimensional phase variables. For instance, the alignment of velocity vectors in a school of fish or a flock of birds can be more realistically set up in three-dimensional space, while the alignment of opinion formation in population dynamics could be multidimensional, in general. We present a generalized D-dimensional swarmalator model, which more accurately captures self-organizing behaviors of a plethora of real-world collectives by self-adaptation of high-dimensional spatial and phase variables. For a more sensible visualization and interpretation of the results, we restrict our simulations to three-dimensional spatial and phase variables. Our model provides a framework for modeling complicated processes such as flocking, schooling of fish, cell sorting during embryonic development, residential segregation, and opinion dynamics in social groups. We demonstrate its versatility by capturing the maneuvers of a school of fish, qualitatively and quantitatively, by a suitable extension of the original model to incorporate appropriate features besides a gallery of its intrinsic self-organizations for various interactions. We expect the proposed high-dimensional swarmalator model to be potentially useful in describing swarming systems and programmable and reconfigurable collectives in a wide range of disciplines, including the physics of active matter, developmental biology, sociology, and engineering.

Effect of higher-order interactions on chimera states in two populations of Kuramoto oscillators.

We investigate the effect of the fraction of pairwise and higher-order interactions on the emergent dynamics of the two populations of globally coupled Kuramoto oscillators with phase-lag parameters. We find that the stable chimera exists between saddle-node and Hopf bifurcations, while the breathing chimera lives between Hopf and homoclinic bifurcations in the two-parameter phase diagrams. The higher-order interaction facilitates the onset of the bifurcation transitions at a much lower disparity between the inter- and intra-population coupling strengths. Furthermore, the higher-order interaction facilitates the spread of breathing chimera in a large region of the parameter space while suppressing the spread of the stable chimera. A low degree of heterogeneity among the phase-lag parameters promotes the spread of both stable chimera and breathing chimera to a large region of the parameter space for a large fraction of the higher-order coupling. In contrast, a large degree of heterogeneity is found to decrease the spread of both chimera states for a large fraction of the higher-order coupling. A global synchronized state is observed above a critical value of heterogeneity among the phase-lag parameters. We have deduced the low-dimensional evolution equations for the macroscopic order parameters using the Ott-Antonsen Ansatz. We have also deduced the analytical saddle-node and Hopf bifurcation curves from the evolution equations for the macroscopic order parameters and found them to match with the bifurcation curves obtained using the software XPPAUT and with the simulation results.

Hebbian and anti-Hebbian adaptation-induced dynamical states in adaptive networks.

We investigate the interplay of an external forcing and an adaptive network, whose connection weights coevolve with the dynamical states of the phase oscillators. In particular, we consider the Hebbian and anti-Hebbian adaptation mechanisms for the evolution of the connection weights. The Hebbian adaptation manifests several interesting partially synchronized states, such as phase and frequency clusters, bump state, bump frequency phase clusters, and forced entrained clusters, in addition to the completely synchronized and forced entrained states. Anti-Hebbian adaptation facilitates the manifestation of the itinerant chimera characterized by randomly evolving coherent and incoherent domains along with some of the aforementioned dynamical states induced by the Hebbian adaptation. We introduce three distinct measures for the strength of incoherence based on the local standard deviations of the time-averaged frequency and the instantaneous phase of each oscillator, and the time-averaged mean frequency for each bin to corroborate the distinct dynamical states and to demarcate the two parameter phase diagrams. We also arrive at the existence and stability conditions for the forced entrained state using the linear stability analysis, which is found to be consistent with the simulation results.

Generalized synchronization in a tritrophic food web metacommunity.

Complete synchronization among the metacommunity is known to elevate the risk of their extinction due to stochasticity and other environmental perturbations. Owing to the inherent heterogeneous nature of the metacommunity, we demonstrate the emergence of generalized synchronization among the patches of dispersally connected tritrophic food web using the framework of an auxiliary system approach and the mutual false nearest neighbor. We find that the critical value of the dispersal rate increases significantly with the size of the metacommunity for both unidirectional and bidirectional dispersals, which in turn corroborates that larger metacommunities are more stable than smaller ones. Further, we find that the critical value of the dispersal for the onset of generalized synchronization is smaller(larger) for bidirectional dispersal than that for unidirectional dispersal for smaller(larger) metacommunities. Most importantly, complete synchronization error remains finite even after the onset of generalized synchronization in a wider range of dispersal rate elucidating that the latter can serve as an early warning signal for the extinction of the metacommunity.

Phase transitions in an adaptive network with the global order parameter adaptation.

We consider an adaptive network of Kuramoto oscillators with purely dyadic coupling, where the adaption is proportional to the degree of the global order parameter. We find only the continuous transition to synchronization via the pitchfork bifurcation, an abrupt synchronization (desynchronization) transition via the pitchfork (saddle-node) bifurcation resulting in the bistable region R_{1}. This is a smooth continuous transition to a weakly synchronized state via the pitchfork bifurcation followed by a subsequent abrupt transition to a strongly synchronized state via a second saddle-node bifurcation along with an abrupt desynchronization transition via the first saddle-node bifurcation resulting in the bistable region R_{2} between the weak and strong synchronization. The transition goes from the bistable region R_{1} to the bistable region R_{2}, and transition from the incoherent state to the bistable region R_{2} as a function of the coupling strength for various ranges of the degree of the global order parameter and the adaptive coupling strength. We also find that the phase-lag parameter enlarges the spread of the weakly synchronized state and the bistable states R_{1} and R_{2} to a large region of the parameter space. We also derive the low-dimensional evolution equations for the global order parameters using the Ott-Antonsen ansatz. Further, we also deduce the pitchfork, first and second saddle-node bifurcation conditions, which is in agreement with the simulation results.

Highly pathogenic avian influenza (H5N1) infection in crows through ingestion of infected crow carcasses.

The present study was aimed to investigate the role of cannibalism in transmission of H5N1 avian influenza virus to house crows (Corvus splendens). Four crows were intranasally inoculated with 108.0 EID50 (A/crow/India/01CA249/2021) H5N1 highly pathogenic avian influenza (HPAI) virus and were observed for 14 days for any overt signs of illness. Two of the infected crows showed signs of wing paralysis, incoordination, and torticollis. For cannibalism experiment, two crows showing clinical signs were euthanized on 14th day post-infection (dpi) and were kept in the isolator and four naïve healthy crows were introduced along with the euthanized crows. The viscera from the infected carcasses were eaten by all the four crows. Oropharyngeal and cloacal swabs were collected up to 14 days to assess virus excretion. All four crows showed clinical signs viz., dullness, reluctance to move with ruffled feathers on 6th day post cannibalism along with neurological signs including incoordination and paralysis of the wings. All the crows gradually recovered after showing clinical signs and were euthanized on 21st day of observation period. Virus excretion was observed from 3rd to 11th day post cannibalism through both oropharyngeal and cloacal routes with maximum shedding through oropharyngeal route. The virus was isolated from lungs and trachea of one the infected crows at 21st day after euthanasia. All the four crows seroconverted against H5N1 virus infection at 14th day post cannibalism. Our study confirms the transmission of H5N1 virus in crows through cannibalism and highlights how H5N1 virus might circulate in a crow colony once they become infected.

Multistable chimera states in a smallest population of three coupled oscillators.

We uncover the emergence of distinct sets of multistable chimera states in addition to chimera death and synchronized states in a smallest population of three globally coupled oscillators with mean-field diffusive coupling. Sequence of torus bifurcations result in the manifestation of distinct periodic orbits as a function of the coupling strength, which in turn result in the genesis of distinct chimera states constituted by two synchronized oscillators coexisting with an asynchronous oscillator. Two subsequent Hopf bifurcations result in homogeneous and inhomogeneous steady states resulting in desynchronized steady states and chimera death state among the coupled oscillators. The periodic orbits and the steady states lose their stability via a sequence of saddle-loop and saddle-node bifurcations finally resulting in a stable synchronized state. We have generalized these results to N coupled oscillators and also deduced the variational equations corresponding to the perturbation transverse to the synchronization manifold and corroborated the synchronized state in the two-parameter phase diagrams using its largest eigenvalue. Chimera states in three coupled oscillators emerge as a solitary state in N coupled oscillator ensemble.

Abrupt symmetry-preserving transition from the chimera state.

We consider two populations of the globally coupled Sakaguchi-Kuramoto model with the same intra- and interpopulations coupling strengths. The oscillators constituting the intrapopulation are identical whereas the interpopulations are nonidentical with a frequency mismatch. The asymmetry parameters ensure the permutation symmetry among the oscillators constituting the intrapopulation and a reflection symmetry among the oscillators constituting the interpopulation. We show that the chimera state manifests by spontaneously breaking the reflection symmetry and also exists in almost in the entire explored range of the asymmetry parameter without restricting to the near π/2 values of it. The saddle-node bifurcation mediates the abrupt transition from the symmetry breaking chimera state to the symmetry-preserving synchronized oscillatory state in the reverse trace, whereas the homoclinic bifurcation mediates the transition from the synchronized oscillatory state to synchronized steady state in the forward trace. We deduce the governing equations of motion for the macroscopic order parameters employing the finite-dimensional reduction by Watanabe and Strogatz. The analytical saddle-node and homoclinic bifurcation conditions agree well with the simulations results and the bifurcation curves.

Solvable Dynamics of Coupled High-Dimensional Generalized Limit-Cycle Oscillators.

We introduce a new model consisting of globally coupled high-dimensional generalized limit-cycle oscillators, which explicitly incorporates the role of amplitude dynamics of individual units in the collective dynamics. In the limit of weak coupling, our model reduces to the D-dimensional Kuramoto phase model, akin to a similar classic construction of the well-known Kuramoto phase model from weakly coupled two-dimensional limit-cycle oscillators. For the practically important case of D=3, the incoherence of the model is rigorously proved to be stable for negative coupling (K<0) but unstable for positive coupling (K>0); the locked states are shown to exist if K>0; in particular, the onset of amplitude death is theoretically predicted. For D≥2, the discrete and continuous spectra for both locked states and amplitude death are governed by two general formulas. Our proposed D-dimensional model is physically more reasonable, because it is no longer constrained by fixed amplitude dynamics, which puts the recent studies of the D-dimensional Kuramoto phase model on a stronger footing by providing a more general framework for D-dimensional limit-cycle oscillators.

Monkeypox: a model-free analysis.

Monkeypox is a zoonotic disease caused by a virus that is a member of the orthopox genus, which has been causing an outbreak since May 2022 around the globe outside of its country of origin Democratic Republic of the Congo, Africa. Here we systematically analyze the data of cumulative infection per day adapting model-free analysis, in particular, statistically using the power law distribution, and then separately we use reservoir computing-based Echo state network (ESN) to predict and forecast the disease spread. We also use the power law to characterize the country-specific infection rate which will characterize the growth pattern of the disease spread such as whether the disease spread reached a saturation state or not. The results obtained from power law method were then compared with the outbreak of the smallpox virus in 1907 in Tokyo, Japan. The results from the machine learning-based method are also validated by the power law scaling exponent, and the correlation has been reported.

Role of limiting dispersal on metacommunity stability and persistence.

The role of dispersal on the stability and synchrony of a metacommunity is a topic of considerable interest in theoretical ecology. Dispersal is known to promote both synchrony, which enhances the likelihood of extinction, and spatial heterogeneity, which favors the persistence of the population. Several efforts have been made to understand the effect of diverse variants of dispersal in the spatially distributed ecological community. Despite that environmental change strongly affects the dispersal, the effects of controlled dispersal on the metacommunity stability and their persistence remain unknown. We study the influence of limiting the immigration using two-patch prey-predator metacommunity at both local and spatial scales. We find that the spread of the inhomogeneous stable steady states (asynchronous states) decreases monotonically upon limiting the predator dispersal. Nevertheless, at the local scale, the spread of the inhomogeneous steady states increases up to a critical value of the limiting factor, favoring the metacommunity persistence, and then starts decreasing for a further decrease in the limiting factor with varying local interaction. Interestingly, limiting the prey dispersal promotes inhomogeneous steady states in a large region of the parameter space, thereby increasing the metacommunity persistence at both spatial and local scales. Further, we show similar qualitative dynamics in an entire class of complex networks consisting of a large number of patches. We also deduce various bifurcation curves and stability conditions for the inhomogeneous steady states, which we find to agree well with the simulation results. Thus, our findings on the effect of the limiting dispersal can help to develop conservation measures for ecological communities.

Exotic states induced by coevolving connection weights and phases in complex networks.

We consider an adaptive network, whose connection weights coevolve in congruence with the dynamical states of the local nodes that are under the influence of an external stimulus. The adaptive dynamical system mimics the adaptive synaptic connections common in neuronal networks. The adaptive network under external forcing displays exotic dynamical states such as itinerant chimeras whose population density of coherent and incoherent domains coevolves with the synaptic connection, bump states, and bump frequency cluster states, which do not exist in adaptive networks without forcing. In addition, the adaptive network also exhibits partial synchronization patterns such as phase and frequency clusters, forced entrained, and incoherent states. We introduce two measures for the strength of incoherence based on the standard deviation of the temporally averaged (mean) frequency and on the mean frequency to classify the emergent dynamical states as well as their transitions. We provide a two-parameter phase diagram showing the wealth of dynamical states. We additionally deduce the stability condition for the frequency-entrained state. We use the paradigmatic Kuramoto model of phase oscillators, which is a simple generic model that has been widely employed in unraveling a plethora of cooperative phenomena in natural and man-made systems.

Influence of asymmetric parameters in higher-order coupling with bimodal frequency distribution.

We investigate the phase diagram of the Sakaguchi-Kuramoto model with a higher-order interaction along with the traditional pairwise interaction. We also introduce asymmetry parameters in both the interaction terms and investigate the collective dynamics and their transitions in the phase diagrams under both unimodal and bimodal frequency distributions. We deduce the evolution equations for the macroscopic order parameters and eventually derive pitchfork and Hopf bifurcation curves. Transition from the incoherent state to standing wave pattern is observed in the presence of the unimodal frequency distribution. In contrast, a rich variety of dynamical states such as the incoherent state, partially synchronized state-I, partially synchronized state-II, and standing wave patterns and transitions among them are observed in the phase diagram via various bifurcation scenarios, including saddle-node and homoclinic bifurcations, in the presence of bimodal frequency distribution. Higher-order coupling enhances the spread of the bistable regions in the phase diagrams and also leads to the manifestation of bistability between incoherent and partially synchronized states even with unimodal frequency distribution, which is otherwise not observed with the pairwise coupling. Further, the asymmetry parameters facilitate the onset of several bistable and multistable regions in the phase diagrams. Very large values of the asymmetry parameters allow the phase diagrams to admit only the monostable dynamical states.

Oscillation quenching in diffusively coupled dynamical networks with inertial effects.

Self-sustained oscillations are ubiquitous and of fundamental importance for a variety of physical and biological systems including neural networks, cardiac dynamics, and circadian rhythms. In this work, oscillation quenching in diffusively coupled dynamical networks including "inertial" effects is analyzed. By adding inertia to diffusively coupled first-order oscillatory systems, we uncover that even small inertia is capable of eradicating the onset of oscillation quenching. We consolidate the generality of inertia in eradicating oscillation quenching by extensively examining diverse quenching scenarios, where macroscopic oscillations are extremely deteriorated and even completely lost in the corresponding models without inertia. The presence of inertia serves as an additional scheme to eradicate the onset of oscillation quenching, which does not need to tailor the coupling functions. Our findings imply that inertia of a system is an enabler against oscillation quenching in coupled dynamical networks, which, in turn, is helpful for understanding the emergence of rhythmic behaviors in complex coupled systems with amplitude degree of freedom.

Quenching of oscillation by the limiting factor of diffusively coupled oscillators.

A simple limiting factor in the intrinsic variable of the normal diffusive coupling is known to facilitate the phenomenon of reviving of oscillation [Zou et al., Nat. Commun. 6, 7709 (2015)2041-172310.1038/ncomms8709], where the limiting factor destabilizes the stable steady states, thereby resulting in the manifestation of the stable oscillatory states. In contrast, in this work we show that the same limiting factor can indeed facilitate the manifestation of the stable steady states by destabilizing the stable oscillatory state. In particular, the limiting factor in the intrinsic variable facilitates the genesis of a nontrivial amplitude death via a saddle-node infinite-period limit (SNIPER) bifurcation and symmetry-breaking oscillation death via a saddle-node bifurcation among the coupled identical oscillators. The limiting factor facilities the onset of symmetric oscillation death among the coupled nonidentical oscillators. It is known that the nontrivial amplitude death state manifests via a subcritical pitchfork bifurcation in general. Nevertheless, here we observe the transition to the nontrivial amplitude death via a SNIPER bifurcation. The in-phase oscillatory state loses its stability via the SNIPER bifurcation, resulting in the manifestation of the nontrivial amplitude death state, whereas the out-of-phase oscillatory state loses its stability via a homoclinic bifurcation, resulting in an unstable oscillatory state. Multistabilities among the various dynamical states are also observed. We have also deduced the evolution equation for the perturbation governing the stability of the observed dynamical states and stability conditions for SNIPER and pitchfork bifurcations. The generic nature of the effect of the limiting factor is also reinforced using two distinct nonlinear oscillators.

Nontrivial amplitude death in coupled parity-time-symmetric Liénard oscillators.

We unravel the collective dynamics exhibited by two coupled nonlinearly damped Liénard oscillators exhibiting parity and time symmetry, which is a classical example of the position-dependent damped systems. The coupled system facilitates the onset of limit-cycle and aperiodic oscillations in addition to large-amplitude oscillations. In particular, a nontrivial amplitude death state emerges as a consequence of balanced linear loss and gain of the coupled PT-symmetric systems, where gain in the amplitude of oscillation in one oscillator is exactly balanced by the loss in the other. Further, quasiperiodic attractors exist in the parameter space of a neutrally stable trivial steady state. We deduce analytical critical curves enclosing the stable regions of a nontrivial fixed point, leading to the manifestation of nontrivial amplitude death state, and neutrally stable trivial steady state. The latter loses its stability leading to the emergence of the former. The analytical critical curves exactly match with the simulation boundaries. There is also a reemergence of dynamical states as a function of the coupling strength and multistability among the observed dynamical states. The basin of attraction provides an explanation for the observed probability of dynamical states.

Metacommunity persistence to environmental change: Stabilizing and destabilizing effects of individual species dispersal.

Ecological communities face a high risk of extinction to climate change which can destabilize ecological systems. In the face of accelerating environmental change, understanding the factors and the mechanisms that stabilize the ecological communities is a central focus in ecology. Although dispersal has been widely used as an important stabilizing process, it remains unclear how individual species dispersal affects the stability and persistence of an ecological community. In this study, using a spatially coupled predator-prey community, we address the effects of individual species dispersal and nutrient enrichment on metacommunity stability in constant and varying environments. We show two contrasting effects of dispersal on metacommunity persistence in temporally constant and varying environments. Specifically, predator dispersal in constant environments shows stronger stability through inhomogeneous (asynchronized) states, whereas prey dispersal shows an increasing extinction risk through a homogeneous (synchronized) state. On the contrary, the metacommunity dynamics in temporally varying environments reveal that predator dispersal causes a local extinction through tracking unstable states and also a delayed shift between dynamical states. Moreover, our results emphasize that metacommunity persistence depends on individual species dispersal and environmental variations. Thus, our findings of the individual species dispersal can help to develop conservation measures that are tailored to varying environmental conditions.

Role of phase-dependent influence function in the Winfree model of coupled oscillators.

We consider a globally coupled Winfree model comprised of a phase-dependent influence function and sensitive function, and unravel the impact of offset and integer parameters, characterizing the shape of the influence function, on the phase diagram of the Winfree model. The decreasing value of the offset parameter decreases the degree of positive phase shift among the oscillators by promoting the negative phase shift, which indeed favors the onset of multistability among the synchronous oscillatory state and asynchronous stable steady states in a large region of the phase diagram. Further, large integer parameters lead to brief pulses of the influence function, which again enhances the effect of the offset parameter. There is an explosive transition to a synchronous oscillatory state from an asynchronous steady state via a Hopf bifurcation. Dynamical transitions and multistability emerge through saddle-node, pitchfork, and homoclinic bifurcations in the phase diagram. We deduce two ordinary differential equations corresponding to the two macroscopic variables from the population of globally coupled Winfree oscillators using the Ott-Antonsen ansatz. We also deduce various bifurcation curves analytically from the reduced low-dimensional macroscopic variables for the exactly solvable case. The analytical curves exactly match the simulation boundaries in the phase diagram.

Experimental infection and pathology of two highly pathogenic avian influenza H5N1 viruses isolated from crow and chicken in house crows (Corvus splendens).

We investigated the experimental infection of two highly pathogenic avian influenza H5N1 viruses isolated from crow (A/crow/Assam/142119/2008) and chicken (A/chicken/Sikkim/151466/2009) in house crows (Corvus splendens). Both viruses caused infection in crows, where four out of six and three out of six crows succumbed to H5N1 infection within 11 days post challenge by crow and chicken viruses, respectively. The major clinical signs in crows were wing paralysis, circling and torticollis. The virus shedding detected from swabs was not persistent in both crow nor chicken viruses. Both viruses were isolated more frequently from oral swabs than from cloacal swabs. Both virus strains were isolated from brain, lungs, heart, liver, pancreas, spleen, large intestines of crows that succumbed to H5N1 infection. The surviving birds seroconverted in response to H5N1 virus infection. Microscopically, both viruses caused coagulative necrosis in pancreas and kidneys. Brain showed gliosis and neuronal degeneration. This experimental study highlights that crows could be infected with H5N1 viruses from different hosts with minor differences in pathogenicity. Therefore, it is imperative to carry out surveillance of highly pathogenic avian influenza H5N1 virus in synanthropic birds along with biosecurity measures to mitigate the H5N1 spread in poultry population. Keywords: chicken virus; crow virus; highly pathogenic avian influenza; house crows.

Symmetry breaking dynamics induced by mean-field density and low-pass filter.

The phenomenon of spontaneous symmetry breaking facilitates the onset of a plethora of nontrivial dynamical states/patterns in a wide variety of dynamical systems. Spontaneous symmetry breaking results in amplitude and phase variations in a coupled identical oscillator due to the breaking of the prevailing permutational/translational symmetry of the coupled system. Nevertheless, the role and the competing interaction of the low-pass filter and the mean-field density parameter on the symmetry breaking dynamical states are unclear and yet to be explored explicitly. The effect of low pass filtering along with the mean-field parameter is explored in conjugately coupled Stuart-Landau oscillators. The dynamical transitions are examined via bifurcation analysis. We show the emergence of a spontaneous symmetry breaking (asymmetric) oscillatory state, which coexists with a nontrivial amplitude death state. Through the basin of attraction, the multi-stable nature of the spontaneous symmetry breaking state is examined, which reveals that the asymmetric distribution of the initial state favors the spontaneous symmetry breaking dynamics, while the symmetric distribution of initial states gives rise to the nontrivial amplitude death state. In addition, the trade-off between the cut-off frequency of the low-pass filter along with the mean-field density induces and enhances the symmetry breaking dynamical states. Global dynamical transitions are discussed as a function of various system parameters. Analytical stability curves corresponding to the nontrivial amplitude death and oscillation death states are deduced.