Search Results (23)

In this paper, a class of two-delay predator–prey models with coefficient-dependent delay is studied. It examines the combined effect of fear-induced delay and post-predation biomass conversion delay on the stability of predator–prey systems. By analyzing the distribution of roots of the characteristic equation, the stability conditions for the internal equilibrium and the existence criteria for Hopf bifurcations are derived. Utilizing normal form theory and the central manifold theorem, the direction of Hopf bifurcations and the stability of periodic solutions are calculated. Finally, numerical simulations are conducted to verify the theoretical findings. This research reveals that varying delays can destabilize the predator–prey system, reflecting the dynamic complexity of real-world ecosystems more realistically. Full article

This paper investigates the Hopf bifurcation of a three-dimensional food chain model with two timedelays, focusing on the synergistic effect of time delays in energy transfer between different trophic levels on the stability of the system. By analyzing the distribution of the roots of the characteristic equation, the stability conditions of the internal equilibrium point and the criterion for the existence of the Hopf bifurcation are established. Using the paradigm theory and the central manifold theorem, explicit formulas for determining the bifurcation direction and the stability of the bifurcation periodic solution are obtained. Numerical simulations verify the theoretical results. This study shows that increasing the time delay will lead to the instability of the food chain model through Hopf bifurcation and produce limit cycle oscillations. This work simulates the asymmetric propagation mode of population fluctuations observed in natural ecosystems, providing a theoretical basis for analyzing the coevolution of complex food webs. Full article

This research explores the dynamics of vegetation patterns under changing environmental conditions, considering the United Nations Sustainable Development Goal 15: “Protect, restore, and promote the sustainable use of terrestrial ecosystems; combat desertification; halt and reverse land degradation; and prevent biodiversity loss”. In this context, this study presents a modeling and nonlinear analysis framework for plant–soil-moisture interactions, including Holling-II functional response and hyperbolic mortality models. The primary goal is to explore how nonlinear soil–water interactions influence vegetation patterns in semi-arid ecosystems. Moreover, the influence of nonlinear soil–water interaction on the establishment of population patterns is investigated. The formation and evolution of these patterns are explored using theoretical analysis and numerical simulations, as well as important factors and critical thresholds. These insights are crucial for addressing desertification, a key challenge in semi-arid regions that threatens biodiversity, ecosystem services, and sustainable land management. The model, which includes environmental parameters such as rainfall, plant growth rates, and soil moisture, was tested using both theoretical analysis and numerical simulations. These characteristics are carefully adjusted to find important thresholds influencing the danger of desertification. Simulation scenarios, run under set initial conditions and varying parameters, yield useful insights into the pattern of patch development under dynamically changing environmental conditions. The findings revealed that changes in environmental conditions, such as rainfall and plant growth rates, prompted Hopf bifurcation, resulting in the production of three distinct patterns: a dotted pattern, a striped pattern, and a combination of both. The creation of these patterns provides essential information about the sustainability of environmental equilibrium. The variation curve of the average plant biomass reveals that the biomass fluctuates around a constant period, with the amplitude initially increasing, then decreasing, and gradually stabilizing. This research provides a solid foundation for addressing desertification risks, using water resources responsibly, and contributing to a better understanding of ecosystem stability. Full article

In this paper, we present novel seasonal carrying capacity prey–predator models with a general functional response, which is that of Crowley–Martin. Seasonality effects are classified into two categories: sudden and periodic perturbations. Models with sudden perturbations are analytically investigated in terms of good and bad circumstances by addressing the existence, positivity, and boundedness of the solution; obtaining the stability conditions for each equilibrium point and the dynamics involving the existence of a limit cycle; determining the Hopf bifurcation with respect to the carrying capacity; and finding the uniform persistence conditions of the models. Moreover, some numerical simulations are performed to demonstrate and validate our theoretical findings. In contrast, models with periodic perturbations are computationally investigated. In analytical findings, the degree of seasonality and the classification of circumstances play a significant role in the uniqueness of the coexistence equilibrium point, the stability of the system, and the existence of a limit cycle. The model with periodic perturbations shows the presence of different dynamics for prey and predator, such as the doubling of the limit cycle and chaos dynamics, so this influence can have a diverse range of possible solutions, which makes the system more enriched with different dynamics. As a result of these findings, many phenomena and changes can be interpreted in ecosystems from an ecological point of view. Full article

The genus Ancistrohaptor was proposed to accommodate monopisthocotylans flatworms parasitic on the gills of species of the genus Triportheus in Manaus, Amazonas state, Brazil. Its main characteristics are (a) an accessory piece of the male copulatory organ composed of two distinct parts; (b) dextral or dextroventral vaginal openings; and (c) large ventral anchors with elongated shafts. A new species of Ancistrohaptor was found to parasitize the gills of Triportheus signatus collected from the Salgado River, Ceará State, Brazil. A new species of Monopisthocotyla was collected and described. Ancistrohaptor forficata sp. n. is primarily characterized by having a male copulatory organ with less than one turn, the presence of an articulated accessory piece with a concave rod-shaped termination, and a free accessory piece that is clamp shaped and bifurcated, as well as a dorsal bar with shading present in its medial part. This is the fourth species description of the genus Ancistrohaptor for fish of the genus Triportheus and the first record for T. signatus and the aquatic ecosystems of the Caatinga domain. Full article

Host–parasitoid systems are an essential area of research in ecology and evolutionary biology due to their widespread occurrence in nature and significant impact on species evolution, population dynamics, and ecosystem stability. In such systems, the host is the organism being attacked by the parasitoid, while the parasitoid depends on the host to complete its life cycle. This paper investigates the effect of parasitoid aggregation attacks on a host in a host–parasitoid model with self-diffusion on two-dimensional coupled map lattices. We assume that in the simulation of biological populations on a plane, the interactions between individuals follow periodic boundary conditions. The primary objective is to analyze the complex dynamics of the host–parasitoid interaction model induced by an aggregation effect and diffusion in a discrete setting. Using the aggregation coefficient k as the bifurcating parameter and applying central manifold and normal form analysis, it has been shown that the system is capable of Neimark–Sacker and flip bifurcations even without diffusion. Furthermore, with the influence of diffusion, the system exhibits pure Turing instability, Neimark–Sacker–Turing instability, and Flip–Turing instability. The numerical simulation section explores the path from bifurcation to chaos through calculations of the maximum Lyapunov exponent and the construction of a bifurcation diagram. The interconversion between different Turing instabilities is simulated by adjusting the timestep and self-diffusion coefficient values, which is based on pattern dynamics in ecological modeling. This contributes to a deeper understanding of the dynamic behaviors driven by aggregation effects in the host–parasitoid model. Full article

In recent decades, there have been many studies on Hopf bifurcation and population stability with time delay. However, the stability and Hopf bifurcation of fractional-order population systems with time delay are lower. In this paper, we discuss the dynamic behavior of a fractional-order three-population model with pregnancy delay using Laplace transform of fractional differential equations, stability and bifurcation theory, and MATLAB software. The specific conditions of local asymptotic stability and Hopf bifurcation for fractional-order time-delay systems are determined. A fractional-order proportional–integral–derivative (PID) controller is applied to the three-population food chain system for the first time. The convergent speed and vibration amplitude of the system can be changed by PID control. For example, after fixing the values of the integral control gain $k_i$ and the differential control gain $k_d$, the amplitude of the system decreases and the convergence speed changes as the proportional control gain $k_p$ decreases. The effectiveness of the PID control strategy in complex ecosystem is proved. The numerical simulation results are in good agreement with the theoretical analysis. The research in this paper has potential application values concerning the management of complex population systems. The bifurcation theory of fractional-order time-delay systems is also enriched. Full article

This paper analyzes the dynamic behavior of a fishery model described by differential algebraic equations. Two patches, namely free fishing area and protected area, are included in the model. The migration of fish is symmetrical, i.e., the fish can migrate between the two patches. It is observed that a singularity-induced bifurcation occurs when the economic benefit of harvesting changes. When the economic benefit is positive, a state feedback controller is added to stabilize the system. Some examples and numerical simulations are presented to verify the theoretical results. In addition, harvesting of prey populations is used as a control measure to obtain the maximum economic benefits and ecological sustainability. The optimal solution is derived by using Pontryagin’s maximum principle. Through extensive numerical simulations, it is shown that the optimal solution is capable of achieving ecosystem sustainability. Full article

Tidal flat plays an important role in coastal development because of its ecological and spatial resources. We take the southern tidal flat in the macro-tidal turbid Hangzhou Bay as an example to study the long-term (1990–2020) evolution of the muddy tidal flat, using remote sensing data and field observational data. The detailed bathymetric elevation of the tidal flat is obtained, using remote sensing images of Landsat and Sentinel-2, combined with the real-time kinematic (RTK) data. The correlation coefficient between the remote sensing data and the RTK data is 0.73. The tidal flat and vegetation areas are affected by reclamation. The total tidal flat area decreased by 467.78 km². The vegetation area declined from 64.98 km² in 2000 to 13.41 km² in 2015 and recovered to 41.62 km² in 2020. The largest change in tidal flat slope occurs in the eastern and western sides of the tidal flat, compared with the wide middle part. The total length of tidal creeks decreased to 45.95 km in 2005 and then increased to 105.83 km in 2020. The middle- and low-grade tidal creeks accounted for 91.4%, with a curvature slightly larger than 1 in 2020. High-grade tidal creeks occur inside the vegetation areas, with less bending and fewer branch points. Vegetation promotes the development of tidal creeks but limits the lateral swing and bifurcation. These results provide a basis for the management of global tidal flat resources and ecosystems. Full article

When confronted with the imminent threat of predation, the prey instinctively employ strategies to avoid being consumed. These anti-predator tactics involve individuals acting collectively to intimidate predators and reduce potential harm during an attack. In the present work, we propose a state-dependent feedback control predator-prey model that incorporates a nonmonotonic functional response, taking into account the anti-predator behavior observed in pest-natural enemy ecosystems within the agricultural context. The qualitative analysis of this model is presented utilizing the principles of impulsive semi-dynamical systems. Firstly, the stability conditions of the equilibria are derived by employing pertinent properties of planar systems. The precise domain of the impulsive set and phase set is determined by considering the phase portrait of the system. Secondly, a Poincaré map is constructed by utilizing the sequence of impulsive points within the phase set. The stability of the order-1 periodic solution at the boundary is subsequently analyzed by an analog of the Poincaré criterion. Additionally, this article presents various threshold conditions that determine both the existence and stability of an order-1 periodic solution. Furthermore, it investigates the existence of order-k ($k\ge 2$) periodic solutions. Finally, the article explores the complex dynamics of the model, encompassing multiple bifurcation phenomena and chaos, through computational simulations. Full article

Forest pests and diseases can diminish forest biodiversity, damage forest ecosystem functions, and have an impact on water conservation. Therefore, it is necessary to analyze the interaction mechanism between plants and pests. In this paper, the prevention and control of a specific pest—namely the larva of Paranthrene tabaniformis (Rott.) (hereinafter referred to as larva)—are studied. Based on the invasion mechanism of the larva in poplar, we establish a delayed differential equation and analyze the existence and stability of equilibria. Next, we assess the existence of a Hopf bifurcation to determine the range of parameters that ensures that the equilibria are stable. Then, we select a set of parameters to verify the results of the stability analysis. Finally, we provide biological explanations and effective theoretical control methods for poplar pests and diseases. Full article

Plankton occupy a vital place in the marine ecosystem due to their essential role. However small or microscopic, their absence can bring the entire life process to a standstill. In this work, we have proposed a prey–predator ecological model consisting of phytoplankton, zooplankton, and fish, incorporating the cannibalistic nature of zooplankton harvesting the fish population. Due to differences in their feeding habits, zooplankton are divided into two sub-classes: herbivorous and carnivorous. The dynamic behavior of the model is examined for each of the possible steady states. The stability criteria of the model have been analyzed from both local and global perspectives. Hopf bifurcation analysis has been accomplished with the growth rate of carnivorous zooplankton using cannibalism as a bifurcation parameter. To characterize the optimal control, we have used Pontryagin’s maximum principle. Subsequently, the optimal system has been derived and solved numerically using an iterative method with Runge–Kutta fourth-order scheme. Finally, to facilitate the interpretation of our mathematical results, we have proceeded to investigate it using numerical simulations. Full article

Two nutrient–phytoplankton–zooplankton (NZP) models for a closed ecosystem that incorporates a delay in nutrient recycling, obtained using the gamma distribution function with one or two degrees of freedom, are analysed. The models are described by systems of ordinary differential equations of four and five dimensions. The purpose of this study is to investigate how the mean delay of the distribution and the total nutrients affect the stability of the equilibrium solutions. Local stability theory and bifurcation theory are used to determine the long-time dynamics of the models. It is found that both models exhibit comparable qualitative dynamics. There are a maximum of three equilibrium points in each of the two models, and at most one of them is locally asymptotically stable. The change of stability from one equilibrium to another takes place through a transcritical bifurcation. In some hypotheses on the functional response, the nutrient–phytoplankton–zooplankton equilibrium loses stability via a supercritical Hopf bifurcation, causing the apparition of a stable limit cycle. The way in which the results are consistent with prior research and how they extend them is discussed. Finally, various application-related consequences of the results of the theoretical study are deduced. Full article

We propose a way of dealing with invasive species or pest control in agriculture. Ecosystems can be modeled via dynamical systems. For their study, it is necessary to establish their possible equilibria. Even a moderately complex system exhibits, in general, multiple steady states. Usually, they are related to each other through transcritical bifurcations, i.e., the system settles to a different equilibrium when some bifurcation parameter crosses a critical threshold. From a situation in which the pest is endemic, it is desirable to move to a pest-free point. The map of the system’s equilibria and their connections via transcritical bifurcations may indicate a path to attain the desired state. However, to force the parameters to cross the critical threshold, some human action is required, and this effort has a cost. The tools of dynamic programming allow the detection of the cheapest path to reach the desired goal. In this paper, an algorithm for the solution to this problem is illustrated. Full article

Two new ecoepidemic models of predator–prey type are introduced. They feature prey that gather in herds. The specific novelty consists of the fact that the prey also has the ability to defend themselves if they are in large numbers. The two deterministic models differ in the way a disease spreading among the ecosystem is transmitted, either by direct contact among infected and susceptible animals or by the intake of a virus present in the environment. Only the disease-free and the endemic equilibrium are allowed, and they are analyzed for feasibility and stability. The boundedness results allow us to gather some results regarding global stability. Persistent oscillations can be triggered when some relevant model parameters cross specific thresholds, causing repeated epidemic outbreaks. Furthermore, the environmental contamination through a free viruses destabilizes the endemic equilibrium and may lead to large amplitude oscillations, which are dangerous because they are potentially harmful to ecosystems. The bifurcation parameters leading to the limit cycle onset are related to the epidemics. For instance, they could be the disease-related mortality and the transmission rates, whether by direct contact among individuals or through the environment. The results of this investigation may provide insights to theoretical ecologists and may provide useful indications for epidemic spread containment. Full article