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.

Secure malicious node detection in flying ad-hoc networks using enhanced AODV algorithm.

In wireless networking, the security of flying ad hoc networks (FANETs) is a major issue, and the use of drones is growing every day. A distributed network is created by a drone network in which nodes can enter and exit the network at any time. Because malicious nodes generate bogus identifiers, FANET is unstable. In this research study, we proposed a threat detection method for detecting malicious nodes in the network. The proposed method is found to be most effective compared to other methods. Malicious nodes fill the network with false information, thereby reducing network performance. The secure ad hoc on-demand distance vector (AODV) that has been suggested algorithm is used for detecting and isolating a malicious node in FANET. In addition, because temporary flying nodes are vulnerable to attacks, trust models based on direct or indirect reliability similar to trusted neighbors have been incorporated to overcome the vulnerability of malicious/selfish harassment. A node belonging to the malicious node class is disconnected from the network and is not used to forward or forward another message. The FANET security performance is measured by throughput, packet loss and routing overhead with the conventional algorithms of AODV (TAODV) and reliable AODV secure AODV power consumption decreased by 16.5%, efficiency increased by 7.4%, and packet delivery rate decreased by 9.1% when compared to the second ranking method. Reduced packet losses and routing expenses by 9.4%. In general, the results demonstrate that, in terms of energy consumption, throughput, delivered packet rate, the number of lost packets, and routing overhead, the proposed secure AODV algorithm performs better than the most recent, cutting-edge algorithms.

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.

Exploration of field-like torque and field-angle tunability in coupled spin-torque nano oscillators for synchronization.

We investigate the influence of field-like torque and the direction of the external magnetic field on a one-dimensional array of serially connected spin-torque nano oscillators (STNOs), having free layers with perpendicular anisotropy, to achieve complete synchronization between them by analyzing the associated Landau-Lifshitz-Gilbert-Slonczewski equation. The obtained results for synchronization are discussed for the cases of 2, 10, and 100 oscillators separately. The roles of the field-like torque and the direction of the external field on the synchronization of the STNOs are explored through the Kuramoto order parameter. While the field-like torque alone is sufficient to bring out global synchronization in the system made up of a small number of STNOs, the direction of the external field is also needed to be slightly tuned to synchronize the one-dimensional array of a large number of STNOs. The formation of complete synchronization through the construction of clusters within the system is identified for the 100 oscillators. The large amplitude synchronized oscillations are obtained for small to large numbers of oscillators. Moreover, the tunability in frequency for a wide range of currents is shown for the synchronized oscillations up to 100 spin-torque oscillators. In addition to achieving synchronization, the field-like torque increases the frequency of the synchronized oscillations. The transverse Lyapunov exponents are deduced to confirm the stable synchronization in coupled STNOs due to the field-like torque and to validate the results obtained in the numerical simulations. The output power of the array is estimated to be enhanced substantially due to complete synchronization by the combined effect of field-like torque and tunability of the field-angle.

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.

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.

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.

Route to extreme events in a parametrically driven position-dependent nonlinear oscillator.

We explore the dynamics of a damped and driven Mathews-Lakshmanan oscillator type model with position-dependent mass term and report two distinct bifurcation routes to the advent of sudden, intermittent large-amplitude chaotic oscillations in the system. We characterize these infrequent and recurrent large oscillations as extreme events (EE) when they are significantly greater than the pre-defined threshold height. In the first bifurcation route, the system exhibits a bifurcation from quasiperiodic (QP) attractor to chaotic attractor via strange non-chaotic (SNA) attractor as a function of damping parameter. In the second route, the chaotic attractor in the form of EE has emerged directly from the QP attractor. Hence, to the best of our knowledge, this is the first study to report the birth of EE from these two distinct bifurcation routes. We also discuss that EE are emerged due to the sudden expansion of the chaotic attractor via interior crisis in the system. Regions of different dynamical states are distinguished using the Lyapunov exponent spectrum. Further, SNA and QP dynamics are determined using the singular spectrum analysis and 0-1 test. The region of EE is characterized using the threshold height.

Coherent Doppler LIDAR with long-duration frequency-modulated pulses for wind sensing.

A coherent Doppler LIDAR (CDL) with long-duration frequency-modulated pulses was demonstrated and validated by analyzing the data observed by a prototype. In traditional CDL using short-duration single-frequency pulses (PCDL; pulsed CDL), there exists a trade-off relationship between distance and velocity resolution. Meanwhile, in earlier work, a theoretical framework of CDL using long-duration frequency-modulated pulses (FMCDL; frequency-modulated CDL) was put forth to eliminate the trade-off. We developed the prototype to be operated as both a PCDL and FMCDL. Analyses of data observed by the PCDL and FMCDL modes showed that the FMCDL worked in good agreement with the PCDL for wind ranging and velocimetry. Furthermore, the performance of the FMCDL in terms of received power and resolution of distance and velocity was quantitatively consistent with ones theoretically expected.

Analysis of COVID-19 in India using a vaccine epidemic model incorporating vaccine effectiveness and herd immunity.

COVID-19 will be a continuous threat to human population despite having a few vaccines at hand until we reach the endemic state through natural herd immunity and total immunization through universal vaccination. However, the vaccine acts as a practical tool for reducing the massive public health problem and the emerging economic consequences that the continuing COVID -19 epidemic is causing worldwide, while the vaccine efficacy wanes. In this work, we propose and analyze an epidemic model of Susceptible-Exposed-Infected-Recovered-Vaccinated population taking into account the rate of vaccination and vaccine waning. The dynamics of the model has been investigated, and the condition for a disease-free endemic equilibrium state is obtained. Further, the analysis is extended to study the COVID-19 spread in India by considering the availability of vaccines and the related critical parameters such as vaccination rate, vaccine efficacy and waning of vaccine's impact on deciding the emerging fate of this epidemic. We have also discussed the conditions for herd immunity due to vaccinated individuals among the people. Our results highlight the importance of vaccines, the effectiveness of booster vaccination in protecting people from infection, and their importance in epidemic and pandemic modeling.

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.

Emerging chimera states under nonidentical counter-rotating oscillators.

Frequency plays a crucial role in exhibiting various collective dynamics in the coexisting corotating and counter-rotating systems. To illustrate the impact of counter-rotating frequencies, we consider a network of nonidentical and globally coupled Stuart-Landau oscillators with additional perturbation. Primarily, we investigate the dynamical transitions in the absence of perturbation, demonstrating that the transition from desynchronized state to cluster oscillatory state occurs through an interesting partial synchronization state in the oscillatory regime. Following this, the system dynamics transits to amplitude death and oscillation death states. Importantly, we find that the observed dynamical states do not preserve the parity (P) symmetry in the absence of perturbation. When the perturbation is increased one can note that the system dynamics exhibits a kind of transition which corresponds to a change from incoherent mixed synchronization to coherent mixed synchronization through a chimera state. In particular, incoherent mixed synchronization and coherent mixed synchronization states completely preserve the P symmetry, whereas the chimera state preserves the P symmetry only partially. To demonstrate the occurrence of such partial symmetry-breaking (chimera) state, we use basin stability analysis and discover that partial symmetry breaking exists as a result of the coexistence of symmetry-preserving and symmetry-breaking behavior in the initial state space. Further, a measure of the strength of P symmetry is established to quantify the P symmetry in the observed dynamical states. Subsequently, the dynamical transitions are investigated in the parametric spaces. Finally, by increasing the network size, the robustness of the chimera state is also inspected, and we find that the chimera state is robust even in networks of larger sizes. We also show the generality of the above results in the related reduced phase. model as well as in other coupled models such as the globally coupled van der Pol and Rössler oscillators.

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.

Analysis of the second wave of COVID-19 in India based on SEIR model.

India was under a grave threat from the second wave of the COVID-19 pandemic particularly in the beginning of May 2021. The situation appeared rather gloomy as the number of infected individuals/active cases had increased alarmingly during the months of May and June 2021 compared to the first wave peak. Indian government/state governments have been implementing various control measures such as lockdowns, setting up new hospitals, and putting travel restrictions at various stages to lighten the virus spread from the initial outbreak of the pandemic. Recently, we have studied the susceptible-exposed-infectious-removed (SEIR) dynamic modeling of the epidemic evolution of COVID-19 in India with the help of appropriate parameters quantifying the various governmental actions and the intensity of individual reactions. Our analysis had predicted the scenario of the first wave quite well. In this present article, we extend our analysis to estimate and analyze the number of infected individuals during the second wave of COVID-19 in India with the help of the above SEIR model. Our findings show that the people's individual effort along with governmental actions such as implementations of curfews and accelerated vaccine strategy are the most important factors to control the pandemic in the present situation and in the future.

Spin torque oscillations triggered by in-plane field.

We study the dynamics of a spin torque nano oscillator that consists of parallelly magnetized free and pinned layers by numerically solving the associated Landau-Lifshitz-Gilbert-Slonczewski equation in the presence of a field-like torque. We observe that an in-plane magnetic field which is applied for a short interval of time (<1 ns) triggers the magnetization to exhibit self-oscillations from low energy initial magnetization state. Also, we confirm that the frequency of oscillations can be tuned over the range ∼25-∼72 GHz by current, even in the absence of field-like torque. We find the frequency enhancement up to 10 GHz by the presence of field-like torque. We determine theQ-factor for different frequencies and show that it increases with frequency. Our analysis with thermal noise confirms that the system is stable against thermal noise and the dynamics is not altered appreciably by it.

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.