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Cyclic dominance is observed in predator-prey interactions, the mating strategy of side-blotched lizards, the overgrowth of marine sessile organisms and competition in microbial populations and many other natural systems. Rock-Paper-Scissor(RPS) is a popular game which demonstrates cyclic dominance. In this paper, we investigate replicator dynamics of RPS-game under logistic growth functions with Allee effect. The results obtained are compared with the case of no Allee effect. Due to Allee effect the number of stable attractors increases in a certain parameter region. The obtained result can be interpreted biologically that diversity of an ecological system increases due to Allee effect. [ABSTRACT FROM AUTHOR]

In this paper, diffusion driven pattern forming instabilities in a predator-prey system with mutually interfering predators described by the Beddington-DeAngelis type functional response, are investigated in the presence of additional food for predators. Conditions for Hopf, Turing and wave instabilities are investigate around the coexisting equilibrium point analytically. Numerical simulation results are presented to show different types of spot, stripe and their mixture patterns. Different spatial domains in the parameter space are plotted. The existence and non-existence of positive, non-constant, steady states of the reaction-diffusion model are established. It is observed that spatio-temporal pattern of a predator prey system can change significantly depending upon the parameters related to additional food. We can conclude from our study, that the reasons of appearance of different spatio-temporal patterns in the real life ecological systems may be due to variation of additional food. [ABSTRACT FROM AUTHOR]

The synchronization behavior of delay coupled chaotic smooth unimodal maps over a ring network with stochastic switching of links at every time step is reported in this paper. It is observed that spatiotemporal synchronization never appears for nearest neighbor connections; however, stochastic switching of connections with homogeneous delay ( τ ) is capable of synchronizing the network to homogeneous steady state or periodic orbit or synchronized chaotically oscillating state depending on the delay parameter, stochasticity parameter and map parameters. Most interestingly, linear stability analysis of the synchronized state is done analytically for unit delay and the value of the critical coupling strength, at which the synchronization occurs is determined analytically. The logistic map r x ( 1 − x ) (a smooth unimodal map) is chosen for numerical simulation purpose. It is found that synchronized steady state or synchronized period-2 orbit is stabilized for delay τ = 1 depending upon the nature of the local map. On the other hand for delay τ = 2 the network is stabilized to the fixed point of the local map. Numerical simulation results are in good agreement with the analytically obtained linear stability analysis results. Another interesting observation is the existence of synchronized chaos in the network for delay τ > 2. Calculating synchronization error and plotting time series data and Poincare first return map and largest Lyapunov exponent the existence of synchronized chaos is confirmed. The results hold good for other smooth unimodal maps also. [ABSTRACT FROM AUTHOR]

In this paper, we have investigated the phenomena of Turing pattern formation in a predator-prey model with habitat complexity in presence of cross diffusion. Using the linear stability analysis, the conditions for the existence of stationary pattern and the existence of Hopf bifurcation are obtained. It is shown analytically that the presence of cross diffusion in the system supports the formation of Turing pattern. Two parameter bifurcation analysis are done analytically and corresponding bifurcation diagrams are presented numerically. A series of simulation results are plotted for different biologically meaningful parameter values. Effects of variation of habitat complexity and the predator mortality rate and birth rate of prey on pattern formation are also reported. It is shown that cross-diffusion can lead to a wide variety of spatial and spatiotemporal pattern formation. It is found that the model exhibits spot and stripe pattern, and coexistence of both spot and strip patterns under the zero flux boundary condition. It is observed that cross-diffusion, habitat complexity, birth rate of prey and predator’s mortality rate play a significant role in the pattern formation of a distributed population system of predator-prey type. [ABSTRACT FROM AUTHOR]

Spatiotemporal dynamics of a predator–prey system in presence of spatial diffusion is investigated in presence of additional food exists for predators. Conditions for stability of Hopf as well as Turing patterns in a spatial domain are determined by making use of the linear stability analysis. Impact of additional food is clear from these conditions. Numerical simulation results are presented in order to validate the analytical findings. Finally numerical simulations are carried out around the steady state under zero flux boundary conditions. With the help of numerical simulations, the different types of spatial patterns (including stationary spatial pattern, oscillatory pattern, and spatiotemporal chaos) are identified in this diffusive predator–prey system in presence of additional food, depending on the quantity, quality of the additional food and the spatial domain and other parameters of the model. The key observation is that spatiotemporal chaos can be controlled supplying suitable additional food to predator. These investigations may be useful to understand complex spatiotemporal dynamics of population dynamical models in presence of additional food. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Highlights: [•] We propose a chaotic food chain model supplying additional food to top-predator. [•] Local and global stability conditions are derived in presence of additional food. [•] Chaos is controlled only by increasing quantity of additional food. [•] System enters into periodic region and depicts Hopf bifurcations supplying additional food. [•] This an application of non-chemical methods for controlling chaos. [Copyright &y& Elsevier]

Abstract: This paper presents synchronization scheme for time-delayed linearly bidirectionally coupled chaotic Chen’s system. The method is based on linear stability analysis of hyperbolic fixed point. Here we derive a generic condition of global chaos synchronization for time-delayed chaotic Chen’s system with linearly bidirectional coupling. The behavior of the system with and without coupling are demonstrated by numerical simulation. [Copyright &y& Elsevier]

Abstract: Several important properties of chaos synchronization of bidirectionally coupled systems remain still unexplored. This paper investigates identical synchronization scheme for generalised linearly bidirectionally coupled unified chaotic system. The Lyapunov stability theory is used to substantiate the results. The study of linearly bidirectionally coupled unified chaotic systems are done first and conditions on coupling parameters for synchronization are derived. Finally, numerical simulation results are presented to show the feasibility and effectiveness of the approach. [Copyright &y& Elsevier]

Abstract: The synchronization threshold in the general form of one way time-delay system is discussed. The synchronization threshold of coupled time-delay chaotic systems can be estimated by two different analytical approaches. One of them is based on the Krasovskii–Lyapunov theory that represents an extension of the second Lyapunov method for delay differential equations. Another approach uses a perturbation theory of large delay time. Based on the Krasovskii–Lyapunov theory, the deduction process and the application range of the synchronization threshold are given. [Copyright &y& Elsevier]

The impacts of additional food for predator on the dynamics of a prey-predator model with prey refuge are investigated. The equilibrium points and their stability behaviours are determined. Hopf bifurcation conditions are derived analytically. Most significantly, existence conditions for unique stable limit cycle in the phase plane are shown analytically. The analytical results are in well agreement with the numerical simulation results. Effects of variation of refuge level as well as the variation of quality and quantity of additional food on the dynamics are reported with the help of bifurcation diagrams. It is found that high quality and high quantity of additional food supports oscillatory coexistence of species. It is observed that predator extinction possibility in high prey refuge ecological systems may be removed by supplying additional food to predator population. The reported theoretical results may be useful to conservation biologist for species conservation in real world ecological systems. [ABSTRACT FROM AUTHOR]