A systematic study of autonomous and nonautonomous predator-prey models for the combined effects of fear, refuge, cooperation and harvesting

Impact of elevated carbon dioxide and temperature on crop yield: A study of autonomous and nonautonomous systems

Agricultural crops are vital for human survival, forming the backbone of global food supply. However, the rising atmospheric carbon dioxide (CO2) level and the increasing temperature relative to the pre-industrial level are poised to impact the yields of essential staple food crops significantly. In this research, we propose and analyze a nonlinear mathematical model to investigate the effects of elevated CO2 and temperature on crop yield. Our model assumes that rising CO2 levels elevate the global average temperature, and the surface temperature initially boosts the growth rate of crops until a threshold is reached, after which the growth rate declines. We also incorporate seasonal variations into the model and perform a comprehensive analytical and numerical analysis of both the autonomous and associated nonautonomous systems. Our findings reveal a critical threshold for anthropogenic CO2 emissions, beyond which the crop yield starts to decrease. Notably, crops with high-temperature tolerance demonstrate higher yields even under elevated CO2 conditions, suggesting a viable strategy for mitigating climate change impacts: developing or utilizing crop varieties with enhanced temperature tolerance. Moreover, our analysis of the nonautonomous system uncovers periodic solutions when the corresponding autonomous system is stable. The nonautonomous system also exhibits complex dynamics, including higher-period oscillations and chaos, when the autonomous system undergoes limit-cycle oscillations. This study provides valuable insights into the interplay between CO2 level, global average surface temperature, and crop yield, offering potential strategies for safeguarding agricultural productivity in the face of climate change.

Bifurcation analysis of autonomous and nonautonomous modified Leslie-Gower models

In ecological systems, the predator-induced fear dampens the prey's birth rate; yet, it fails to extinguish their population, as they endure and survive even under significant fear-induced costs. In this study, we unveil a modified Leslie-Gower predator-prey model by incorporating the fear of predators, cooperative hunting, and predator-taxis sensitivity. We embark upon an exploration of the positivity and boundedness of solutions, unearthing ecologically viable equilibrium points and their stability conditions governed by the model parameters. Delving deeper, we unravel the scenario of transcritical, saddle-node, Hopf, Bogdanov-Takens, and generalized-Hopf bifurcations within the system's intricate dynamics. Additionally, we observe the bistable nature of the system under some parametric conditions. Further, the nonautonomous extension of our model introduces the intriguing interplay of seasonality in some crucial parameters. We establish a set of sufficient conditions that guarantee the permanence of the seasonally driven system. By conducting a numerical study on the seasonally forced model, we observe a myriad of phenomena manifesting the predator-prey dynamics. Notably, periodic solutions, higher periodic solutions, and bursting patterns emerge, alongside intriguing chaotic dynamics. Specifically, seasonal variations of the predator-taxis sensitivity and hunting cooperation can lead to the extinction of prey species and even the control of chaotic (higher periodic) solutions through the generation of a simple periodic solution. Remarkably, the seasonal forcing has the capacity to govern the chaotic behavior, leading to an exceptionally quasi-periodic arrangement in both prey and predator populations.

Fear effect in a three-species food chain model with generalist predator

Within the framework of a food web, the foraging behavior of meso-carnivorous species is influenced by fear responses elicited by higher trophic level species, consequently diminishing the fecundity of these species. In this study, we investigate a three-species food chain model comprising of prey, an intermediate predator, and a top predator. We assume that both the birth rate and intraspecies competition of prey are impacted by fear induced by the intermediate predator. Additionally, the foraging behavior of the intermediate predator is constrained due to the presence of the top predator. It is essential to note that the top predators exhibit a generalist feeding behavior, encompassing food sources beyond the intermediate predators. The study systematically determines all feasible equilibria of the proposed model and conducts a comprehensive stability analysis of these equilibria. The investigation reveals that the system undergoes Hopf bifurcation concerning various model parameters. Notably, when other food sources significantly contribute to the growth of the top predators, the system exhibits stable behavior around the interior equilibrium. Our findings indicate that the dynamic influence of fear plays a robust role in stabilizing the system. Furthermore, a cascading effect within the system, stemming from the fear instigated by top predators, is observed and analyzed. Overall, this research sheds light on the intricate dynamics of fear-induced responses in shaping the stability and behavior of multi-species food web systems, highlighting the profound cascading effects triggered by fear mechanisms in the ecosystem.

Translating Virtual Prey-Predator Interaction to Real-World Robotic Environments: Enabling Multimodal Sensing and Evolutionary Dynamics

Prey-predator interactions play a pivotal role in elucidating the evolution and adaptation of various organism's traits. Numerous approaches have been employed to study the dynamics of prey-predator interaction systems, with agent-based methodologies gaining popularity. However, existing agent-based models are limited in their ability to handle multi-modal interactions, which are believed to be crucial for understanding living organisms. Conversely, prevailing prey-predator integration studies often rely on mathematical models and computer simulations, neglecting real-world constraints and noise. These elusive attributes, challenging to model, can lead to emergent behaviors and embodied intelligence. To bridge these gaps, our study designs and implements a prey-predator interaction scenario that incorporates visual and olfactory sensory cues not only in computer simulations but also in a real multi-robot system. Observed emergent spatial-temporal dynamics demonstrate successful transitioning of investigating prey-predator interactions from virtual simulations to the tangible world. It highlights the potential of multi-robotics approaches for studying prey-predator interactions and lays the groundwork for future investigations involving multi-modal sensory processing while considering real-world constraints.

Role reversal in a stage-structured prey-predator model with fear, delay, and carry-over effects

The present work highlights the reverse side of the same ecological coin by considering the counter-attack of prey on immature predators. We assume that the birth rate of prey is affected by the fear of adult predators and its carry-over effects (COEs). Next, we introduce two discrete delays to show time lag due to COEs and fear-response. We observe that the existence of a positive equilibrium point and the stability of the prey-only state is independent of fear and COEs. Furthermore, the necessary condition for the co-existence of all three species is determined. Our system experiences several local and global bifurcations, like, Hopf, saddle-node, transcritical, and homoclinic bifurcation. The simultaneous variation in the attack rate of prey and predator results in the Bogdanov-Takens bifurcation. Our numerical results explain the paradox of enrichment, chaos, and bi-stability of node-focus and node-cycle types. The system, with and without delay, is analyzed theoretically and numerically. Using the normal form method and center manifold theorem, the conditions for stability and direction of Hopf-bifurcation are also derived. The cascade of predator attacks, prey counter-attacks, and predator defense exhibit intricate dynamics, which sheds light on ecological harmony.

Effect of Fear, Treatment, and Hunting Cooperation on an Eco-Epidemiological Model: Memory Effect in Terms of Fractional Derivative

In this paper, we have studied a fractional-order eco-epidemiological model incorporating fear, treatment, and hunting cooperation effects to explore the memory effect in the ecological system through Caputo-type fractional-order derivative. We have studied the behavior of different equilibrium points with the memory effect. The proposed system undergoes through Hopf bifurcation with respect to the memory parameter as the bifurcation parameter. We perform numerical simulations for different values of the memory parameter and some of model parameters. In the numerical results, it appears that the system is exhibiting a stable behavior from a period or chaotic nature with the increase in the memory effect. The system also exhibits two transcritical bifurcations with respect to the growth rate of the prey. At low values of prey's growth, all species go to extinction, at moderate values of prey's growth, only preys (susceptible and infected) can survive, and at higher values of prey's growth, all species survive simultaneously. The paper ended with some recommendations.

Impacts of lockdown on the dynamics of forestry biomass, wildlife species and control of atmospheric pollution

In this paper, we have formulated and analysed a mathematical model to investigate the impacts of lockdown on the dynamics of forestry biomass, wildlife species and pollution. For this purpose, we have considered a nonlinear system of four ordinary differential equations representing rates of change of the density of forestry biomass, the density of wildlife species, the concentration of pollutants and lockdown. Conditions for the existence, uniqueness and local stability of all equilibria along with the global stability of the interior equilibrium point are derived. Furthermore, conditions that influence the persistence of the system are obtained. By formulating an optimal control problem, the optimal strategies for minimizing the cost of implementation of lockdown as well as the concentration of pollutants are also studied. Numerical simulations are carried out to verify and validate our analytical findings. By this study, we have observed that implementation of lockdown for a sufficient period of time minimizes excessive harvesting of both forestry biomass and wildlife species and the concentration of pollutants in the environment. It is also found that lockdown policy is effective in the optimal control of atmospheric pollution. Therefore, lockdown plays a significant role in the dynamics of forestry biomass, wildlife species and control of pollution in the environment.