Existence of spatial patterns in reaction–diffusion systems incorporating a prey refuge

In real-world ecosystem, studies on the mechanisms of spatiotemporal pattern formation in a system of interacting populations deserve special attention for its own importance in contemporary theoretical ecology. The present investigation deals with the spatial dynamical system of a two-dimensional continuous diffusive predator–prey model involving the influence of intra-species competition among predators with the incorporation of a constant proportion of prey refuge. The linear stability analysis has been carried out and the appropriate condition of Turing instability around the unique positive interior equilibrium point of the present model system has been determined. Furthermore, the existence of the various spatial patterns through diffusion-driven instability and the Turing space in the spatial domain have been explored thoroughly. The results of numerical simulations reveal the dynamics of population density variation in the formation of isolated groups, following spotted or stripe-like patterns or coexistence of both the patterns. The results of the present investigation also point out that the prey refuge does have significant influence on the pattern formation of the interacting populations of the model under consideration

Biological control via "ecological" damping: An approach that attenuates non-target effects

In this work we develop and analyze a mathematical model of biological control to prevent or attenuate the explosive increase of an invasive species population in a three-species food chain. We allow for finite time blow-up in the model as a mathematical construct to mimic the explosive increase in population, enabling the species to reach "disastrous" levels, in a finite time. We next propose various controls to drive down the invasive population growth and, in certain cases, eliminate blow-up. The controls avoid chemical treatments and/or natural enemy introduction, thus eliminating various non-target effects associated with such classical methods. We refer to these new controls as "ecological damping", as their inclusion dampens the invasive species population growth. Further, we improve prior results on the regularity and Turing instability of the three-species model that were derived in earlier work. Lastly, we confirm the existence of spatio-temporal chaos

Dynamical Complexity of a Spatial Phytoplankton-Zooplankton Model with an Alternative Prey and Refuge Effect

The spatiotemporal dynamics of a phytoplankton-zooplankton model with an alternative prey and refuge effect is investigated mathematically and numerically. The stability of the equilibrium point and the traveling wave solution of the phytoplankton-zooplankton model are described based on theoretical mathematical work, which provides the basis of the numerical simulation. The numerical analysis shows that refuges have a strong effect on the spatiotemporal dynamics of the model according to the pattern formation. These results may help us to understand prey-predator interactions in water ecosystems. They are also relevant to research into phytoplankton-zooplankton ecosystems

Ecological system with fear induced group defence and prey refuge

In this study, we investigate the dynamics of a spatial and non spatial prey-predator interaction model that includes the following: (i) fear effect incorporated in prey birth rate; (ii) group defence of prey against predators; and (iii) prey refuge. We provide comprehensive mathematical analysis of extinction and persistence scenarios for both prey and predator species. To better explore the dynamics of the system, a thorough investigation of bifurcation analysis has been performed using fear level, prey birth rate, and prey death rate caused by intra-prey competition as bifurcation parameter. All potential occurrences of bi-stability dynamics have also been investigated for some relevant sets of parametric values. Our numerical evaluations show that high levels of fear can stabilize the prey-predator system by ruling out the possibility of periodic solutions. Also, our model Hopf bifurcation is subcritical in contrast to traditional prey-predator models, which ignore the cost of fear and have supercritical Hopf bifurcations in general. In contrast to the general trend, predator species go extinct at higher values of prey birth rates. We have also found that, contrary to the typical tendency for prey species to go extinct, both prey and predator populations may coexist in the system as intra-prey competition level grows noticeably. The stability and Turing instability of associated spatial model have also been investigated analytically. We also perform the numerical simulation to observe the effect of different parameters on the density distribution of species. Different types of spatiotemporal patterns like spot, mixture of spots and stripes have been observed via variation of time evolution, diffusion coefficient of predator population, level of fear factor and prey refuge. The fear level parameter (k) has a great impact on the spatial dynamics of model system

Pattern formation and bifurcation analysis of delay induced fractional-order epidemic spreading on networks

The spontaneous emergence of ordered structures, known as Turing patterns, in complex networks is a phenomenon that holds potential applications across diverse scientific fields, including biology, chemistry, and physics. Here, we present a novel delayed fractional-order susceptible-infected-recovered-susceptible (SIRS) reaction-diffusion model functioning on a network, which is typically used to simulate disease transmission but can also model rumor propagation in social contexts. Our theoretical analysis establishes the Turing instability resulting from delay, and we support our conclusions through numerical experiments. We identify the unique impacts of delay, average network degree, and diffusion rate on pattern formation. The primary outcomes of our study are: (i) Delays cause system instability, mainly evidenced by periodic temporal fluctuations; (ii) The average network degree produces periodic oscillatory states in uneven spatial distributions; (iii) The combined influence of diffusion rate and delay results in irregular oscillations in both time and space. However, we also find that fractional-order can suppress the formation of spatiotemporal patterns. These findings are crucial for comprehending the impact of network structure on the dynamics of fractional-order systems.Comment: 23 pages, 9 figure

Optimal harvesting policy of a prey–predator model with Crowley–Martin-type functional response and stage structure in the predator

In this paper, a three-dimensional dynamical model consisting of a prey, a mature predator, and an immature predator is proposed and analysed. The interaction between prey and mature predator is assumed to be of the Crowley–Martin type, and both the prey and mature predator are harvested according to catch-per-unit-effort (CPUE) hypothesis. Steady state of the system is obtained, stability analysis (local and global both) are discussed to explore the long-time behaviour of the system. The optimal harvesting policy is also discussed with the help of Pontryagin's maximum principle. The harvesting effort is taken as an effective control instrument to preserve prey and predator and to maintain them at an optimal level

Review on carbonation study of reinforcement concrete incorporating with bacteria as self-healing approach

This study carried out a comprehensive review to determine the carbonation process that causes the most deterioration and destruction of concrete. The carbonation mechanism involved using carbon dioxide (CO2 ) to penetrate the concrete pore system into the atmosphere and reduce the alkalinity by decreasing the pH level around the reinforcement and initiation of the corrosion process. The use of bacteria in the concrete was to increase the pH of the concrete by producing urease enzyme. This technique may help to maintain concrete alkalinity in high levels, even when the carbonation process occurs, because the CO2 accelerates to the concrete and then converts directly to calcium carbonate, CaCO3 . Consequently, the self-healing of the cracks and the pores occurred as a result of the carbonation process and bacteria enzyme reaction. As a result of these reactions, the concrete steel is protected, and the concrete properties and durability may improve. However, there are several factors that control carbonation which have been grouped into internal and external factors. Many studies on carbonation have been carried out to explore the effect of bacteria to improve durability and concrete strength. However, an in-depth literature review revealed that the use of bacteria as a self-healing mechanism can still be improved upon. This review aimed to highlight and discuss the possibility of applying bacteria in concrete to improve reinforcement concrete