Selenium - An environmentally friendly micronutrient in agroecosystem in the modern era: An overview of 50-year findings.

Agricultural productivity is constantly being forced to maintain yield stability to feed the enormously growing world population. However, shrinking arable and nutrient-deprived soil and abiotic and biotic stressor (s) in different magnitudes put additional challenges to achieving global food security. Though well-defined, the concept of macro, micronutrients, and beneficial elements is from a plant nutritional perspective. Among various micronutrients, selenium (Se) is essential in small amounts for the life cycle of organisms, including crops. Selenium has the potential to improve soil health, leading to the improvement of productivity and crop quality. However, Se possesses an immense encouraging phenomenon when supplied within the threshold limit, also having wide variations. The supplementation of Se has exhibited promising outcomes in lessening biotic and abiotic stress in various crops. Besides, bulk form, nano-Se, and biogenic-Se also revealed some merits and limitations. Literature suggests that the possibilities of biogenic-Se in stress alleviation and fortifying foods are encouraging. In this article, apart from adopting a combination of a conventional extensive review of the literature and bibliometric analysis, the authors have assessed the journey of Se in the "soil to spoon" perspective in a diverse agroecosystem to highlight the research gap area. There is no doubt that the time has come to seriously consider the tag of beneficial elements associated with Se, especially in the drastic global climate change era.

Stability analysis of synchronization in long-range temporal networks using theory of dichotomy.

Most of the previous studies on the stability analysis of synchronization in static or time-varying networks are based on the master stability function approach, which is a semi-analytical concept. The necessary and sufficient conditions for synchronization in time-varying networks are challenging problems since the last few years. We focus on the stability analysis of synchronization in time-varying networks, particularly long-range networks. The use of dichotomy theory to derive sufficient conditions for synchronization in this context is an interesting approach. The incorporation of long-range interactions adds complexity and might lead to larger regions of synchronization, providing valuable insights into the dynamics of such networks. Analyzing the co-action of the time-varying nature in the network topology and long-range interactions is a relevant and challenging task, especially when the network is not synchronized. This work appears to explore the interplay between these factors and their impact on synchronization. Additionally, the numerical study considering long-range connections governed by a power-law within the framework of an Erdös-Rényi random network is a practical way to validate and test the analytical results. It is good to see that we are exploring the effects of varying parameters such as rewiring probability, coupling strength, and power-law exponent on the synchronization state.

Directional synchrony among self-propelled particles under spatial influence.

Synchronization is one of the emerging collective phenomena in interacting particle systems. Its ubiquitous presence in nature, science, and technology has fascinated the scientific community over the decades. Moreover, a great deal of research has been, and is still being, devoted to understand various physical aspects of the subject. In particular, the study of interacting active particles has led to exotic phase transitions in such systems which have opened up a new research front-line. Motivated by this line of work, in this paper, we study the directional synchrony among self-propelled particles. These particles move inside a bounded region, and crucially their directions are also coupled with spatial degrees of freedom. We assume that the directional coupling between two particles is influenced by the relative spatial distance which changes over time. Furthermore, the nature of the influence is considered to be both short and long-ranged. We explore the phase transition scenario in both the cases and propose an approximation technique which enables us to analytically find the critical transition point. The results are further supported with numerical simulations. Our results have potential importance in the study of active systems like bird flocks, fish schools, and swarming robots where spatial influence plays a pertinent role.

Eco-evolutionary cyclic dominance among predators, prey, and parasites.

Predator-prey interactions are one of ecology's central research themes, but with many interdisciplinary implications across the social and natural sciences. Here we consider an often-overlooked species in these interactions, namely parasites. We first show that a simple predator-prey-parasite model, inspired by the classical Lotka-Volterra equations, fails to produce a stable coexistence of all three species, thus failing to provide a biologically realistic outcome. To improve this, we introduce free space as a relevant eco-evolutionary component in a new mathematical model that uses a game-theoretical payoff matrix to describe a more realistic setup. We then show that the consideration of free space stabilizes the dynamics by means of cyclic dominance that emerges between the three species. We determine the parameter regions of coexistence as well as the types of bifurcations leading to it by means of analytical derivations as well as by means of numerical simulations. We conclude that the consideration of free space as a finite resource reveals the limits of biodiversity in predator-prey-parasite interactions, and it may also help us in the determination of factors that promote a healthy biota.

Resetting-mediated navigation of an active Brownian searcher in a homogeneous topography.

Designing navigation strategies for search-time optimization remains of interest in various interdisciplinary branches in science. Herein, we focus on active Brownian walkers in noisy and confined environments, which are mediated by one such autonomous strategy, namely stochastic resetting. As such, resetting stops the motion and compels the walkers to restart from the initial configuration intermittently. The resetting clock is operated externally without any influence from the searchers. In particular, the resetting coordinates are either quenched (fixed) or annealed (fluctuating) over the entire topography. Although the strategy relies upon simple governing laws of motion, it shows a significant ramification for the search-time statistics, in contrast to the search process conducted by the underlying reset-free dynamics. Using extensive numerical simulations, we show that the resetting-driven protocols enhance the performance of these active searchers. This, however, depends robustly on the inherent search-time fluctuations, measured by the coefficient of variation of the underlying reset-free process. We also explore the effects of different boundaries and rotational diffusion constants on the search-time fluctuations in the presence of resetting. 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 from queuing systems, computer science and randomized numerical algorithms, to active living systems such as enzyme turnover and backtracking recovery of RNA polymerases in gene expression, make resetting-based strategies universally promising.

Evolutionarily stable strategies to overcome Allee effect in predator-prey interaction.

Every successful species invasion is facilitated by both ecological and evolutionary mechanisms. The evolution of population's fitness related traits acts as functional adaptations to Allee effects. This trade-off increases predatory success at an expense of elevated death rate of potential predators. We address our queries employing an eco-evolutionary modeling approach that provides a means of circumventing inverse density-dependent effect. In the absence of evolution, the ecological system potentially exhibits multi-stable configurations under identical ecological conditions by allowing different bifurcation scenarios with the Allee effect. The model predicts a high risk of catastrophic extinction of interacting populations around different types of saddle-node bifurcations resulting from the increased Allee effect. We adopt the game-theoretic approach to derive the analytical conditions for the emergence of evolutionarily stable strategy (ESS) when the ecological system possesses asymptotically stable steady states as well as population cycles. We establish that ESSs occur at those values of adopted evolutionary strategies that are local optima of some functional forms of model parameters. Overall, our theoretical study provides important ecological insights in predicting successful biological invasions in the light of evolution.

Neuronal synchronization in time-varying higher-order networks.

A potential issue of interest is figuring out how the combination of temporal and higher-order interactions influences the collective dynamics of the brain, specifically, neuronal synchronization. Motivated by this, here we consider an ensemble of neurons interacting with each other through gap junctions, modeled by temporal higher-order networks (simplicial complexes), and study the emergence of complete neuronal synchronization. We find that the critical synaptic strength for achieving neuronal synchronization with time-varying higher-order interaction is relatively lower than that with temporal pairwise interactions or static many-body interactions. Our study shows that neuronal synchronization can occur even in the sole presence of higher-order, time-varying interactions. We also find that the enhancement in neuronal synchronization in temporal higher-order structure is highly related to the density of group interactions among the neurons. Furthermore, to characterize the local stability of the synchronous solution, we use the master stability function approach, which shows that the numerical findings are in good agreement with the analytically derived conditions.

Flocking and swarming in a multi-agent dynamical system.

Over the past few decades, the research community has been interested in the study of multi-agent systems and their emerging collective dynamics. These systems are all around us in nature, such as bacterial colonies, fish schools, and bird flocks, as well as in technology, such as microswimmers and robotics, to name a few. Flocking and swarming are two key components of the collective behaviors of multi-agent systems. In flocking, the agents coordinate their direction of motion, but in swarming, they congregate in space to organize their spatial position. We propose a minimal mathematical model of a locally interacting multi-agent system where the agents simultaneously swarm in space and exhibit flocking behavior. Various cluster structures are found depending on the interaction range. When the coupling strength value exceeds a crucial threshold, flocking behavior is observed. We do in-depth simulations and report the findings by changing the other parameters and with the incorporation of noise.

Swarmalators on a ring with uncorrelated pinning.

We present a case study of swarmalators (mobile oscillators) that move on a 1D ring and are subject to pinning. Previous work considered the special case where the pinning in space and the pinning in the phase dimension were correlated. Here, we study the general case where the space and phase pinning are uncorrelated, both being chosen uniformly at random. This induces several new effects, such as pinned async, mixed states, and a first-order phase transition. These phenomena may be found in real world swarmalators, such as systems of vinegar eels, Janus matchsticks, electrorotated Quincke rollers, or Japanese tree frogs.

Dimension reduction in higher-order contagious phenomena.

We investigate epidemic spreading in a deterministic susceptible-infected-susceptible model on uncorrelated heterogeneous networks with higher-order interactions. We provide a recipe for the construction of one-dimensional reduced model (resilience function) of the N-dimensional susceptible-infected-susceptible dynamics in the presence of higher-order interactions. Utilizing this reduction process, we are able to capture the microscopic and macroscopic behavior of infectious networks. We find that the microscopic state of nodes (fraction of stable healthy individual of each node) inversely scales with their degree, and it becomes diminished due to the presence of higher-order interactions. In this case, we analytically obtain that the macroscopic state of the system (fraction of infectious or healthy population) undergoes abrupt transition. Additionally, we quantify the network's resilience, i.e., how the topological changes affect the stable infected population. Finally, we provide an alternative framework of dimension reduction based on the spectral analysis of the network, which can identify the critical onset of the disease in the presence or absence of higher-order interactions. Both reduction methods can be extended for a large class of dynamical models.

Extreme rotational events in a forced-damped nonlinear pendulum.

Since Galileo's time, the pendulum has evolved into one of the most exciting physical objects in mathematical modeling due to its vast range of applications for studying various oscillatory dynamics, including bifurcations and chaos, under various interests. This well-deserved focus aids in comprehending various oscillatory physical phenomena that can be reduced to the equations of the pendulum. The present article focuses on the rotational dynamics of the two-dimensional forced-damped pendulum under the influence of the ac and dc torque. Interestingly, we are able to detect a range of the pendulum's length for which the angular velocity exhibits a few intermittent extreme rotational events that deviate significantly from a certain well-defined threshold. The statistics of the return intervals between these extreme rotational events are supported by our data to be spread exponentially at a specific pendulum's length beyond which the external dc and ac torque are no longer sufficient for a full rotation around the pivot. The numerical results show a sudden increase in the size of the chaotic attractor due to interior crisis, which is the source of instability that is responsible for triggering large amplitude events in our system. We also notice the occurrence of phase slips with the appearance of extreme rotational events when the phase difference between the instantaneous phase of the system and the externally applied ac torque is observed.

Direction-dependent noise-induced synchronization in mobile oscillators.

Synchronization among uncoupled oscillators can emerge when common noise is applied on them and is famously known as noise-induced synchronization. In previous studies, it was assumed that common noise may drive all the oscillators at the same time when they are static in space. Understanding how to develop a mathematical model that apply common noise to only a fraction of oscillators is of significant importance for noise-induced synchronization. Here, we propose a direction-dependent noise field model for noise-induced synchronization of an ensemble of mobile oscillators/agents, and the effective noise on each moving agent is a function of its direction of motion. This enables the application of common noise if the agents are oriented in the same direction. We observe not only complete synchronization of all the oscillators but also clustered states as a function of the ensemble density beyond a critical value of noise intensity, which is a characteristic of the internal dynamics of the agents. Our results provide a deeper understanding on noise-induced synchronization even in mobile agents and how the mobility of agents affects the synchronization behaviors.

Synchronization Induced by Layer Mismatch in Multiplex Networks.

Heterogeneity among interacting units plays an important role in numerous biological and man-made complex systems. While the impacts of heterogeneity on synchronization, in terms of structural mismatch of the layers in multiplex networks, has been studied thoroughly, its influence on intralayer synchronization, in terms of parameter mismatch among the layers, has not been adequately investigated. Here, we study the intralayer synchrony in multiplex networks, where the layers are different from one other, due to parameter mismatch in their local dynamics. In such a multiplex network, the intralayer coupling strength for the emergence of intralayer synchronization decreases upon the introduction of impurity among the layers, which is caused by a parameter mismatch in their local dynamics. Furthermore, the area of occurrence of intralayer synchronization also widens with increasing mismatch. We analytically derive a condition under which the intralayer synchronous solution exists, and we even sustain its stability. We also prove that, in spite of the mismatch among the layers, all the layers of the multiplex network synchronize simultaneously. Our results indicate that a multiplex network with mismatched layers can induce synchrony more easily than a multiplex network with identical layers.

Intralayer and interlayer synchronization in multiplex network with higher-order interactions.

Recent developments in complex systems have witnessed that many real-world scenarios, successfully represented as networks, are not always restricted to binary interactions but often include higher-order interactions among the nodes. These beyond pairwise interactions are preferably modeled by hypergraphs, where hyperedges represent higher-order interactions between a set of nodes. In this work, we consider a multiplex network where the intralayer connections are represented by hypergraphs, called the multiplex hypergraph. The hypergraph is constructed by mapping the maximal cliques of a scale-free network to hyperedges of suitable sizes. We investigate the intralayer and interlayer synchronizations of such multiplex structures. Our study unveils that the intralayer synchronization appreciably enhances when a higher-order structure is taken into consideration in spite of only pairwise connections. We derive the necessary condition for stable synchronization states by the master stability function approach, which perfectly agrees with the numerical results. We also explore the robustness of interlayer synchronization and find that for the multiplex structures with many-body interaction, the interlayer synchronization is more persistent than the multiplex networks with solely pairwise interaction.

Controlling the spontaneous firing behavior of a neuron with astrocyte.

Mounting evidence in recent years suggests that astrocytes, a sub-type of glial cells, not only serve metabolic and structural support for neurons and synapses but also play critical roles in the regulation of proper functioning of the nervous system. In this work, we investigate the effect of astrocytes on the spontaneous firing activity of a neuron through a combined model that includes a neuron-astrocyte pair. First, we show that an astrocyte may provide a kind of multistability in neuron dynamics by inducing different firing modes such as random and bursty spiking. Then, we identify the underlying mechanism of this behavior and search for the astrocytic factors that may have regulatory roles in different firing regimes. More specifically, we explore how an astrocyte can participate in the occurrence and control of spontaneous irregular spiking activity of a neuron in random spiking mode. Additionally, we systematically investigate the bursty firing regime dynamics of the neuron under the variation of biophysical facts related to the intracellular environment of the astrocyte. It is found that an astrocyte coupled to a neuron can provide a control mechanism for both spontaneous firing irregularity and burst firing statistics, i.e., burst regularity and size.

Oscillation suppression and chimera states in time-varying networks.

Complex network theory has offered a powerful platform for the study of several natural dynamic scenarios, based on the synergy between the interaction topology and the dynamics of its constituents. With research in network theory being developed so fast, it has become extremely necessary to move from simple network topologies to more sophisticated and realistic descriptions of the connectivity patterns. In this context, there is a significant amount of recent works that have emerged with enormous evidence establishing the time-varying nature of the connections among the constituents in a large number of physical, biological, and social systems. The recent review article by Ghosh et al. [Phys. Rep. 949, 1-63 (2022)] demonstrates the significance of the analysis of collective dynamics arising in temporal networks. Specifically, the authors put forward a detailed excerpt of results on the origin and stability of synchronization in time-varying networked systems. However, among the complex collective dynamical behaviors, the study of the phenomenon of oscillation suppression and that of other diverse aspects of synchronization are also considered to be central to our perception of the dynamical processes over networks. Through this review, we discuss the principal findings from the research studies dedicated to the exploration of the two collective states, namely, oscillation suppression and chimera on top of time-varying networks of both static and mobile nodes. We delineate how temporality in interactions can suppress oscillation and induce chimeric patterns in networked dynamical systems, from effective analytical approaches to computational aspects, which is described while addressing these two phenomena. We further sketch promising directions for future research on these emerging collective behaviors in time-varying networks.

Taming non-stationary chimera states in locally coupled oscillators.

The imperfect traveling chimera (ITC) state is a novel non-stationary chimera pattern in which the incoherent domain of oscillators spreads into the coherent domain. We investigate the ITC state in locally coupled pendulum oscillators with heterogeneous driving forces. We introduce the heterogeneous phase value in the driving forces by two different ways, namely, the random phase from uniform distribution and random phase directions with identical amplitude. We discover two transition mechanisms from ITC to coherent state through traveling chimera-like state by taking the two different phase heterogeneity. The transition phenomena are investigated using cylindrical and polar coordinate phase spaces. In the numerical study, we propose a quantitative measurement named "spatiotemporal consistency" strength for distinguishing the ITC from the traveling one. Our research facilitates the exploration of potential applications of heterogeneous interactions in neuroscience.

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 that 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.

Extreme events in a complex network: Interplay between degree distribution and repulsive interaction.

The role of topological heterogeneity in the origin of extreme events in a network is investigated here. The dynamics of the oscillators associated with the nodes are assumed to be identical and influenced by mean-field repulsive interactions. An interplay of topological heterogeneity and the repulsive interaction between the dynamical units of the network triggers extreme events in the nodes when each node succumbs to such events for discretely different ranges of repulsive coupling. A high degree node is vulnerable to weaker repulsive interactions, while a low degree node is susceptible to stronger interactions. As a result, the formation of extreme events changes position with increasing strength of repulsive interaction from high to low degree nodes. Extreme events at any node are identified with the appearance of occasional large-amplitude events (amplitude of the temporal dynamics) that are larger than a threshold height and rare in occurrence, which we confirm by estimating the probability distribution of all events. Extreme events appear at any oscillator near the boundary of transition from rotation to libration at a critical value of the repulsive coupling strength. To explore the phenomenon, a paradigmatic second-order phase model is used to represent the dynamics of the oscillator associated with each node. We make an annealed network approximation to reduce our original model and, thereby, confirm the dual role of the repulsive interaction and the degree of a node in the origin of extreme events in any oscillator associated with a node.

Eco-evolutionary dynamics of cooperation in the presence of policing.

Ecology and evolution are inherently linked, and studying a mathematical model that considers both holds promise of insightful discoveries related to the dynamics of cooperation. In the present article, we use the prisoner's dilemma (PD) game as a basis for long-term apprehension of the essential social dilemma related to cooperation among unrelated individuals. We upgrade the contemporary PD game with an inclusion of evolution-induced act of punishment as a third competing strategy in addition to the traditional cooperators and defectors. In a population structure, the abundance of ecologically-viable free space often regulates the reproductive opportunities of the constituents. Hence, additionally, we consider the availability of free space as an ecological footprint, thus arriving at a simple eco-evolutionary model, which displays fascinating complex dynamics. As possible outcomes, we report the individual dominance of cooperators and defectors as well as a plethora of mixed states, where different strategies coexist followed by maintaining the diversity in a socio-ecological framework. These states can either be steady or oscillating, whereby oscillations are sustained by cyclic dominance among different combinations of cooperators, defectors, and punishers. We also observe a novel route to cyclic dominance where cooperators, punishers, and defectors enter a coexistence via an inverse Hopf bifurcation that is followed by an inverse period doubling route.