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Self-organized vegetation patterns are an amazing aspect of dryland ecosystems; in addition to being visually appealing, patterns control how these water-deprived systems react to escalating environmental stress. Although there is a wide variety of vegetation patterns, little is known about the mechanisms behind spiral patterns. The well-known models that explain other vegetation patterns such stripes, rings, and fairy circles cannot account for these spirals. Here we have adopted a modeling approach in which the interplay between herbivore grazing and vegetation is found to be the reason why spirals form. To comprehend the nonlinear dependence of grazing on the availability vegetation, we have introduced a grazing term that gets saturated when forage is abundant. To account for the impact of the spatial nonhomogeneity in vegetation layout, it is thought that grazing is dependent on mean vegetation density rather than density at a single site. Results show how the system dynamics is changed fundamentally depending on the different types of grazing response. Incorporation of nonlocality into the herbivore grazing leads to spiral-shaped vegetation patterns only in natural grazing scenarios; however, no patterning is seen in human controlled herbivory. Overall, our research points to the nonlocal, nonlinear grazing behavior of herbivores as one of the major driving forces for the development of spiral patterns.

Dry-land ecosystems have become a matter of grave concern, due to the growing threat of land degradation and bioproductivity loss. Self-organized vegetation patterns are a remarkable characteristic of these ecosystems; apart from being visually captivating, patterns modulate the system response to increasing environmental stress. Empirical studies hinted that herbivory is one the key regulatory mechanisms behind pattern formation and overall ecosystem functioning. However, most of the mathematical models have taken a mean-field strategy to grazing; foraging has been considered to be independent of spatial distribution of vegetation. To this end, an extended version of the celebrated plant-water model due to Klausmeier has been taken as the base here. To encompass the effect of heterogeneous vegetation distribution on foraging intensity and subsequent impact on entire ecosystem, grazing is considered here to depend on spatially weighted average vegetation density instead of density at a particular point. Moreover, varying influence of vegetation at any location over gazing elsewhere is incorporated by choosing a suitable averaging function. A comprehensive analysis demonstrates that inclusion of spatial nonlocality alters the understanding of system dynamics significantly. The grazing ecosystem is found to be more resilient to increasing aridity than it was anticipated to be in earlier studies on nonlocal grazing. The system response to rising environmental pressure is also observed to vary depending on the grazer. Obtained results also suggest the possibility of multistability due to the history dependence of the system response. Overall, this work indicates that the spatial heterogeneity in grazing intensity has a decisive role to play in the functioning of water-limited ecosystems.

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 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 the 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. The results are found to be consistent with the investigation carried out with a continuous time Hindmarsh-Rose neuron model. Furthermore, the role of hyperparameters like spectral radius and leaking parameter of ESN on the prediction process has been examined. Finally, we explain the underlying mechanism responsible for observing these differences in the prediction in a degree correlated network.

This work considers a two-dimensional hyperbolic reaction-diffusion system with different inertia and explores criteria for various instabilities, like a wave, Turing, and Hopf, both theoretically and numerically. It is proven that wave instability may occur in a two-species hyperbolic reaction-diffusion system with identical inertia if the diffusion coefficients of the species are nonidentical but cannot occur if diffusion coefficients are identical. Wave instability may also arise in a two-dimensional hyperbolic reaction-diffusion system if the diffusivities of the species are equal, which is never possible in a parabolic reaction-diffusion system, provided the inertias are different. Interestingly, Turing instability is independent of inertia, but the stability of the corresponding local system depends on the inertia. Theoretical results are demonstrated with an example where the local interaction is represented by the Schnakenberg system.

In this study, we consider a scale-free network of nonidentical Chialvo neurons, coupled through electrical synapses. For sufficiently strong coupling, the system undergoes a transition from completely out of phase synchronized to phase synchronized state. The principal focus of this study is to investigate the effect of the degree of assortativity over the synchronization transition process. It is observed that, depending on assortativity, bistability between two asymptotically stable states allows one to develop a hysteresis loop which transforms the phase transition from second order to first order. An expansion in the area of hysteresis loop is noticeable with increasing degree-degree correlation in the network. Our study also reveals that effective frequencies of nodes simultaneously go through a continuous or sudden transition to the synchronized state with the corresponding phases. Further, we examine the robustness of the results under the effect of network size and average degree, as well as diverse frequency setup. Finally, we investigate the dynamical mechanism in the process of generating explosive synchronization. We observe a significant impact of lower degree nodes behind such phenomena: in a positive assortative network the low degree nodes delay the synchronization transition.

In ecology, the intra- and inter-specific competition between individuals of mobile species for shared resources is mostly non-local; i.e., competition at any spatial position will not only be dependent on population at that position, but also on population in neighboring regions. Therefore, models that assume competition to be restricted to the individuals at that position only are actually oversimplifying a crucial physical process. For the past three decades, researchers have established the necessity of considering spatial non-locality while modeling ecological systems. Despite this ecological importance, studies incorporating this non-local nature of resource competition in an aquatic ecosystem are surprisingly scarce. To this end, the celebrated Scheffer's tri-trophic minimal model has been considered here as a base model due to its efficacy in describing the pelagic ecosystem with least complexity. It is modified into an integro-reaction-diffusion system to include the effect of non-local competition by introducing a weighted spatial average with a suitable influence function. A detailed analysis shows that the non-locality may have a destabilizing effect on underlying nutrient-plankton-fish dynamics. A local system in a stable equilibrium state can lose its stability through spatial Hopf and Turing bifurcations when strength of a non-local interaction is strong enough, which eventually generates a large range of spatial patterns. The relationship between a non-local interaction and fish predation has been established, which shows that fish predation contributes in damping of plankton oscillations. Overall, results obtained here manifest the significance of non-locality in aquatic ecosystems and its possible contribution to the phenomena of "spatial patchiness."

The effects of the time delay on the stability of different synchronized states of a globally coupled network are investigated. Conditions for the stability of the synchronized fixed points, synchronized periodic orbits, or synchronized chaos in a network of globally coupled chaotic smooth maps over a ring lattice with a homogeneous delay are derived analytically. Our analysis reveals that the stability properties of the synchronized dynamics are significantly different for odd and even time delays. The conditions for the stability of a synchronized fixed point and synchronized period-2 orbits for both odd and even delays are determined analytically. The range of parameter values for the stability of synchronized chaos has been calculated for a unit delay. All theoretical results are illustrated with the help of numerical examples.

Context: Mild cognitive impairment (MCI) is an under-diagnosed health problem in the community. Cognitive screening tools are widely used for MCI detection, but many of them lack sensitivity and specificity in MCI detection. On the basis of literature review, Short test of mental status (STMS) was selected for the present purpose., Aims: The present study purports to standardize STMS for using as a cognitive screening tool in MCI detection in the community-living elderly people in Kolkata., Materials and Methods: Data were collected from 102 community-living elderly people from the city of Kolkata using the purposive method of sampling. MCI was diagnosed using the Peterson's criteria of MCI as the gold standard. A semi-structured demographic proforma, clock-drawing test (CDT), and the Groningen Activity Restriction Scale (GARS) were used for the purpose. Finally, STMS was administered., Statistical Analysis: Statistical computation was done using the SPSS 21. Descriptive statistics, receiver operating curve analysis, and binary logistic regression were used for statistical analysis of the data., Results and Conclusion: STMS emerged as a sensitive and specific cognitive screening tool in the detection of MCI in the current cultural setting. It was also found to be more suited for the purpose than CDT. A score of 34.5 with a sensitivity of 97.5 and a specificity of 90.3% were selected for the optimum cutoff score for the detection of MCI in the present population. With a unit increase in STMS score, the odds of getting diagnosed with MCI were found to be reduced by 48.5%., Competing Interests: There are no conflicts of interest.

The synchronization behavior of coupled chaotic discontinuous maps over a ring network with dynamic random connections is reported in this paper. It is observed that random rewiring stabilizes one of the two strongly unstable fixed points of the local map. Depending on initial conditions, the network synchronizes to different unstable fixed points, which signifies the existence of synchronized multistability in the complex network. Moreover, the length of discontinuity of the local map has an important role in generating windows of different synchronized fixed points. Synchronized fixed point and synchronized periodic orbits are found in the network depending on coupling strength and different parameter values of the local map. We have identified the existence of period subtracting bifurcation with respect to coupling strength in the network. The range of coupling strength for the occurrence of synchronized multistable spatiotemporal fixed points is determined. This range strongly depends upon the dynamic rewiring probability and also on the local map.

Allochthonous inputs are important sources of productivity in many food webs and their influences on food chain model demand further investigations. In this paper, assuming the existence of allochthonous inputs for intermediate predator, a food chain model is formulated with disease in the prey. The stability and persistence conditions of the equilibrium points are determined. Extinction criterion for infected prey population is obtained. It is shown that suitable amount of allochthonous inputs to intermediate predator can control infectious disease of prey population, provided initial intermediate predator population is above a critical value. This critical intermediate population size increases monotonically with the increase of infection rate. It is also shown that control of infectious disease of prey is possible in some cases of seasonally varying contact rate. Dynamical behaviours of the model are investigated numerically through one and two parameter bifurcation analysis using MATCONT 2.5.1 package. The occurrence of Hopf and its continuation curves are noted with the variation of infection rate and allochthonous food availability. The continuation curves of limit point cycle and Neimark Sacker bifurcation are drawn by varying the rate of infection and allochthonous inputs. This study introduces a novel natural non-toxic method for controlling infectious disease of prey in a food chain model., (Copyright © 2015 Elsevier Ltd. All rights reserved.)

We examine the effects of supplying additional food to predator in a gestation delay induced predator-prey system with habitat complexity. Additional food works in favor of predator growth in our model. Presence of additional food reduces the predatory attack rate to prey in the model. Supplying additional food we can control predator population. Taking time delay as bifurcation parameter the stability of the coexisting equilibrium point is analyzed. Hopf bifurcation analysis is done with respect to time delay in presence of additional food. The direction of Hopf bifurcations and the stability of bifurcated periodic solutions are determined by applying the normal form theory and the center manifold theorem. The qualitative dynamical behavior of the model is simulated using experimental parameter values. It is observed that fluctuations of the population size can be controlled either by supplying additional food suitably or by increasing the degree of habitat complexity. It is pointed out that Hopf bifurcation occurs in the system when the delay crosses some critical value. This critical value of delay strongly depends on quality and quantity of supplied additional food. Therefore, the variation of predator population significantly effects the dynamics of the model. Model results are compared with experimental results and biological implications of the analytical findings are discussed in the conclusion section., (Copyright © 2015 Elsevier Inc. All rights reserved.)

Choice of interaction function is one of the most important parts for modelling a food chain. Many models have been proposed as a diseased-prey predator model with Holling type-I or type-II or type-III interactions, but there is no model with general Holling type interactions. In this paper, we study a diseased prey-predator model with general Holling type interactions. Local stability conditions of equilibrium points are derived. We obtain the permanence and impermanence conditions of the system. The conditions for global stability of the system are also derived. The system exhibits limit cycle, period-2, higher periodic oscillations and chaotic behaviour for different values of Holling parameters. One parameter bifurcation analysis is done with respect to general Holling parameters and infection rate. We utilize the MATCONT package to analyse the detailed bifurcation scenario as the two important interaction parameters are varied. It is interesting to note that a diseased system becomes a disease free system for proper choice of interaction functions. Our results give an idea for constructing a realistic food chain model through proper choice of general Holling parameters., (Copyright © 2013 Elsevier Inc. All rights reserved.)

Necessity to find a non-chemical method of disease control is being increasingly felt due to its eco-friendly nature. In this paper the role of alternative food as a disease controller in a disease induced predator-prey system is studied. Stability criteria and the persistence conditions for the system are derived. Bifurcation analysis is done with respect to rate of infection. The main goal of this study is to show the non-trivial consequences of providing alternative food in a disease induced predator-prey system. Numerical simulation results illustrate that there exists a critical infection rate above which disease free system cannot be reached in absence of alternative food whereas supply of suitable alternative food makes the system disease free up to certain infection level. We have computed the disease free regions in various parametric planes. This study is aimed to introduce a new non-chemical method for controlling disease in a predator-prey system., (Copyright © 2012 Elsevier Inc. All rights reserved.)

We investigate the spatiotemporal dynamics of a lattice of coupled chaotic maps whose coupling connections are dynamically rewired to random sites with probability p ; namely, at any instance of time, with probability p a regular link is switched to a random one. In a range of weak coupling, where spatiotemporal chaos exists for regular lattices (i.e., for p=0 ), we find that p>0 yields synchronized periodic orbits. Further, we observe that this regularity occurs over a window of p values, beyond which the basin of attraction of the synchronized cycle shrinks to zero. Thus we have evidence of an optimal range of randomness in coupling connections, where spatiotemporal regularity is efficiently obtained. This is in contrast to the commonly observed monotonic increase of synchronization with increasing p , as seen, for instance, in the strong-coupling regime of the very same system.