Nonlinear Harvester Research Articles

Harvesting strategies in ecological systems: Evaluating their efficiency in infection dominance

In population biology, the interplay between prey and predators in the presence of infection can give rise to complex dynamics. On the flip side, implementing harvesting is an infection control measure. In the present work, we use the dynamical system theory to discuss the dynamics of the harvested prey–predator system in the presence of infection in prey species. Detailed mathematical and numerical evaluations have been presented to discuss the susceptible‐free state, infection‐free state, predator‐free state, species coexistence, stability, and occurrence of various bifurcations (saddle‐node, transcritical, and Hopf bifurcation). The study reveals the impact of harvesting parameters on the dynamics. Interestingly, we observe that an infection‐free state could be achieved by varying the harvesting parameter under all three harvesting schemes (linear, quadratic, and nonlinear). Moreover, with the help of reproduction number, we claim that linear harvesting is more effective in controlling the infection than quadratic and nonlinear harvesting provided the half‐saturation constant for nonlinear harvesting is greater than a threshold value ; otherwise, nonlinear harvesting is more effective. Also, the system can support more susceptible prey in the presence of harvesting. The present theoretical study suggests different threshold values of implemented harvesting to control the disease.

Bifurcation of a Leslie–Gower Predator–Prey Model with Nonlinear Harvesting and a Generalist Predator

A Leslie–Gower predator–prey model with nonlinear harvesting and a generalist predator is considered in this paper. It is shown that the degenerate positive equilibrium of the system is a cusp of codimension up to 4, and the system admits the cusp-type degenerate Bogdanov–Takens bifurcation of codimension 4. Moreover, the system has a weak focus of at least order 3 and can undergo degenerate Hopf bifurcation of codimension 3. We verify, through numerical simulations, that the system admits three different stable states, such as a stable fixed point and three limit cycles (the middle one is unstable), or two stable fixed points and two limit cycles. Our results reveal that nonlinear harvesting and a generalist predator can lead to richer dynamics and bifurcations (such as three limit cycles or tristability); specifically, harvesting can cause the extinction of prey, but a generalist predator provides some protection for the predator in the absence of prey.

Bistability and bifurcations for a food chain model with nonlinear harvesting of top predator

In this paper, we study a prey–predator–top predator food chain model with nonlinear harvesting of top predator. We have derived two important thresholds: the top predator extinction threshold and the coexistence threshold. We found that the top predator will die out if the nonlinear harvesting from predator to top predator is larger than the top predator extinction threshold. On the other hand, the prey, predator and top predator coexist if the nonlinear harvesting from predator to top predator is less than the coexistence threshold. While the parameter value of nonlinear harvesting from predator to top predator is between two critical thresholds, the system displays bistability phenomena, implying that the top predator species either die out or exist with the prey and predator species, which largely depend on the initial condition. Thus, a bistable interval exists between two critical thresholds, which is a significant phenomenon for the model. Meanwhile, we performed bifurcation analysis for the model, showing that the system would arise backward/forward bifurcation and saddle-node bifurcation and Hopf bifurcation. Finally, we performed numerical simulations to verify the theoretical analysis.

Bifurcation Analysis of a Predator-Prey Model Incorporating Non-Linear Harvesting and Group Defense

Bifurcation Analysis of a Predator-Prey Model Incorporating Non-Linear Harvesting and Group Defense

Dynamics of autonomous and nonautonomous Leslie–Gower model for the impacts of fear and its carry‐over effects including predator harvesting

Recently, certain biological field experiments and research findings have revealed that predators not only reduce prey populations through direct predation (lethal effect) but also indirectly affect the growth rate of prey by inducing fear; these nonlethal effects can be carried over seasons or generations. In this paper, we proposed an autonomous and a nonautonomous Leslie–Gower model incorporating some biological factors such as fear and its carry‐over effects, prey refuge, and nonlinear predator harvesting. In the autonomous model, first, we examined the well‐posedness, positivity solutions, and their boundedness. Also, it is shown that new equilibrium points emerge and disappear with the change in intrinsic growth rate of predator. Further, we compute and analyzed the local and global stability at the interior equilibrium points. Furthermore, Hopf bifurcation and direction and stability of limit cycle at interior equilibrium points are established. Moreover, the sensitivity analysis of the biological parameters is carried out numerically with two statistical methods via Latin hypercube sampling and partial rank correlation coefficients. It was found that at the small values of fear factor, carry‐over effect, and refuge behavior of prey parameters, the autonomous system exhibits oscillatory behavior, whereas for small values of prey birth rate and harvesting effort, the system remains stable. However, when intrinsic growth rate of predator increases from a low value to a higher value, the system shows transition from stability to instability and back to stability. We also explore the effects of seasonal variations in biological parameters in the nonautonomous model. Additionally, we investigate the theoretical existence of positive periodic solutions using the continuation theorem. The influences of seasonal variations in some parameters such as prey's birth rate, fear, and its carry‐over effects; refuge behavior of prey; intrinsic growth rate of predator; and harvesting effort are then numerically investigated. The results reveal the emergence of positive periodic solutions and bursting patterns in the seasonally forced model.

Some Bifurcations of Codimensions 1 and 2 in a Discrete Predator–Prey Model with Non-Linear Harvesting

This paper delves into the dynamics of a discrete-time predator–prey system. Initially, it presents the existence and stability conditions of the fixed points. Subsequently, by employing the center manifold theorem and bifurcation theory, the conditions for the occurrence of four types of codimension 1 bifurcations (transcritical bifurcation, fold bifurcation, flip bifurcation, and Neimark–Sacker bifurcation) are examined. Then, through several variable substitutions and the introduction of new parameters, the conditions for the existence of codimension 2 bifurcations (fold–flip bifurcation, 1:2 and 1:4 strong resonances) are derived. Finally, some numerical analyses of two-parameter planes are provided. The two-parameter plane plots showcase interesting dynamical behaviors of the discrete system as the integral step size and other parameters vary. These results unveil much richer dynamics of the discrete-time model in comparison to the continuous model.

Bistability in a predator–prey model characterized by the Crowley–Martin functional response: Effects of fear, hunting cooperation, additional foods and nonlinear harvesting

This study focuses on unraveling key factors influencing predator–prey interactions with Crowley–Martin functional response. Specifically, it explores the roles of additional food sources, harvesting practices, hunting cooperation, fear and its carry-over effects. We analyze equilibrium points and their stability properties through rigorous mathematical methods. Numerical illustrations showcase a diverse range of bifurcations including Hopf, saddle–node, and transcritical, providing a comprehensive understanding of the system’s dynamics. We find that the collaboration among predators during hunting induces instability in the system, leading to the emergence of population cycles from a stable state. Further, we place emphasis on investigating the impact of seasonal forcing by introducing time-varying parameters into our model. We reveal the emergence of periodic solutions, higher periodic solutions and chaotic dynamics due to the seasonal variations of the prey’s birth rate and the degree of hunting cooperation. We also emphasize the significance of incorporating different periodicity of seasonally forced parameters, leading to a more precise understanding of predator–prey dynamics.

Potential of coupled array harvester in enhanced energy harvesting.

Harvesting energy from nonlinear systems has been at the centre of research in the energy harvesting community. Many such proposed systems are single nonlinear harvester. While these systems show an increase in bandwidth of harvesting frequency, overall, they are not effective enough in power generation. This article studies power harvesting and frequency bandwidth characteristics of an array of harvesters. Multiple harvesters are considered with linear and nonlinear coupling between the harvesters. The phenomena of internal resonance (IR) and stochastic resonance (SR) are reported. The IR in multiple coupled nonlinear harvesters is explored using multiple-scale analysis. A parametric study is conducted to demonstrate the effect of coupling strength, frequency mistuning, innate nonlinearity and other parameters. The parametric study helped establish effective ways to increase bandwidth. Moreover, a stochastically loaded linearly coupled bistable harvester array is numerically analysed to find the effect of coupling strength and array size on the phenomenon of SR and on the system's harvesting performance. Through these studies, the potential of multiple coupled nonlinear harvesters in enhanced energy harvesting is demonstrated under both harmonic and stochastic excitation.This article is part of the theme issue 'Celebrating the 15th anniversary of the Royal Society Newton International Fellowship'.

Global bifurcation analysis and derivation of an optimal harvesting policy of a prey–predator model with Holling type-IV functional scheme

ABSTRACT This paper establishes a prey–predator model with a Holling type IV functional response and proportional harvesting in prey species and nonlinear harvesting in predator species. We provide a completely local and global bifurcation analysis of the model to characterize some meaningful results that may emerge from the interaction of biological resources. The proposed model exhibits various complex behaviors involving heteroclinic and homoclinic orbits, and we prove analytically that it also undergoes transcritical, Hopf, and Bogdanov–Takens bifurcations in the prey–predator plane. Moreover, the system is unfolded to compute the bifurcation curves, highlighting the critical dynamics by perturbing two bifurcation parameters near the cusp. Furthermore, from the economic point of view, the bionomic equilibrium of the system is studied, and optimal harvesting policy is derived using the Pontryagin’s maximum principle. Numerical simulations are presented to verify our analytical results.

Effect of fear and non-linear predator harvesting on a predator–prey system in presence of environmental variability

In this paper, we have proposed and analyzed a predator–prey system introducing the cost of predation fear into the prey reproduction with Holling type-II functional response in the stochastic environment with the consideration of non-linear harvesting on predators. The system experiences Transcritical, Saddle–node, Hopf, and Bogdanov-Taken (BT) bifurcation with respect to the intrinsic growth rate and competition rate of the prey populations. We have discussed the existence and uniqueness of positive global solution of the stochastic model with the help of Ito’s integral formula and the long-term behavior of the solution is derived here. The existence of stationary distribution and explicit form of the density function is established here when only prey populations survive or both populations. We have shown that due to high fluctuation, the regime changes from one stable state to another state when bistability occurs in the system. The paper ends with some conclusions.

Optimizing power-efficiency dynamics in ambient energy harvesting: Exploring trade-offs, linearity, and synergy

As the demand for low-power electronics and IoT devices grows, ambient energy harvesting appears to be a promising alternative for powering such systems in the long run. However, optimizing power and efficiency concurrently in such systems is challenging, involving balancing a number of variables. This paper investigates the optimization of power and efficiency in ambient energy harvesting systems focusing on nonlinear oscillator electromechanical harvesters subjected to multiplicative time-correlated ambient noise. Through extensive numerical simulations, we reveal distinct relationships between power and efficiency, influenced by various parameters. We observe autonomous stochastic resonance phenomena, elucidating a linear power-efficiency trend for small noise correlation time under fixed noise variance but limiting simultaneous power and efficiency optimization beyond a threshold. Under fixed noise strength, there is a trade-off between power and efficiency. Additionally, damping strength, piezoelectric parameters, and capacitor charging time impact power and efficiency linearly. These insights enhance understanding of power efficiency dynamics in ambient energy harvesting, thereby offering practical recommendations for parameter selection to maximize both power output and efficiency in the next generation of electronics.

Study of the interference fringes-caustic region interaction in a topological Young's interferometer.

Herein, an analysis of the optical field emerging from a topological Young's interferometer is conducted. The interferometer consists of two 3D-slit shape curves and is studied by projecting it onto a trihedral reference system. From the projection, Airy, Pearcey, and cusped-type beams emerge. The optical field of these beams is organized around its caustic region. The interference between these types of beams presents interesting physical properties, which can be derived from the interaction between the interference fringes and the caustic regions. One property of the interaction is the irradiance flow, which induces a long-distance interaction between the caustic regions. Another property is the bending of the interference fringes toward the caustic regions, which acts as a sink. Due to the adiabatic features of the caustic regions, the interaction between the fringes-caustic and caustic irradiance is studied using a predator-prey model, which leads to a logistic-type differential equation with nonlinear harvesting. The stability analysis of this equation is in good agreement with the theoretical and experimental results.

Dynamics of a Predator–Prey System with Impulsive Stocking Prey and Nonlinear Harvesting Predator at Different Moments

In this article, we study a predator–prey system, which includes impulsive stocking prey and a nonlinear harvesting predator at different moments. Firstly, we derive a sufficient condition of the global asymptotical stability of the predator–extinction periodic solution utilizing the comparison theorem of the impulsive differential equations and the Floquet theory. Secondly, the condition, which is to maintain the permanence of the system, is derived. Finally, some numerical simulations are displayed to examine our theoretical results and research the effect of several important parameters for the investigated system, which shows that the period of the impulse control and impulsive perturbations of the stocking prey and nonlinear harvesting predator have a significant impact on the behavioral dynamics of the system. The results of this paper give a reliable tactical basis for actual biological resource management.

Spatio-temporal dynamics in a delayed prey–predator model with nonlinear prey refuge and harvesting

In the current study, we introduce a model for the temporal and spatial interactions between prey and predator. The model incorporates a nonlinear refuge mechanism for prey, along with linear harvesting of prey and nonlinear harvesting for predators. Initially, we examined the well-posed nature of the model by analyzing the presence of all feasible equilibria and investigating the corresponding dynamics. Following that, we delve into the dynamics of the temporal model, focusing specifically on aspects such as uniform boundedness, permanence, and stability of viable equilibria. We demonstrate analytically that the proposed model experiences transcritical, saddle–node, Hopf, and Bogdanov–Takens bifurcations. It shows a variety of intricate dynamics involving Generalized Hopf and double Hopf. Then, discrete-time delay effects arising from the gestation of predator species have been incorporated into the temporal system. Hopf bifurcation for the delay parameter was detected in this investigation. Subsequently, we established conditions for self-diffusion instability and Turing instability in the spatiotemporal model, both with and without delay, employing the homogeneous Neumann boundary condition. Moreover, the discussion of sensitivity analysis (PRCC) serves to illustrate how crucial parameters influence the dynamics of the system. In addition, we conduct numerical simulations aiming to corroborate and validate the analytical results obtained.

Identifying numerical bifurcation structures of codimensions 1 and 2 in interacting species system

The present study has focused on the examination of a Holling type III nonlinear mathematical model that incorporates the influence of fear and Michaelis–Menten‐type predator harvesting. The incorporation of fear with respect to the prey species has been observed to result in a reduction in the survival probability of the prey population and a concurrent reduction in the reproduction rate of the prey species. The existence and stability of ecologically significant equilibria have been ascertained through mathematical analysis. Emphasis within the proposed model primarily centers on numerical bifurcations of codimensions 1 and 2. Numerical validation has been performed on all simulated outcomes within the feasible range of parametric values. Dynamical characteristics of the model have subsequently undergone investigation through a series of numerical simulations, successfully revealing various forms of local and global bifurcations. In addition to the identification of saddle‐node, Hopf, Bogdanov–Takens, transcritical, cusp, homoclinic, and limit point cycle (LPC) bifurcations, the model has also demonstrated bistability and global asymptotic stability. These bifurcation phenomena serve as illustrative examples of the intricate dynamical behavior inherent to the model. Numerical validation through graphical representations has been utilized to elucidate the effects of factors such as fear, nonlinear predator harvesting, and predation rate on the dynamics of the interacting species under different parametric conditions.

On the stability of a Caputo fractional order predator-prey framework including Holling type-II functional response along with nonlinear harvesting in predator

In this study, we look at a fractional-order two-species predator-prey framework that uses Caputo Sense's fractional derivative to try to understand its dynamics, which include a simplified Holling type II functional response and nonlinear harvesting in the predator. Initially, we establish certain mathematical facts, such as the solutions of fractional order dynamical systems being unique, non-negative, bounded, and existing. The dissipativeness of the FDE system solution is addressed. Our investigation also includes a look at the local stability requirements for every possible equilibrium point. As a bifurcation constraint, the order of derivatives has been considered in our discussion of the existence condition of Hopf bifurcation. Our analysis has been strengthened by the incorporation of fractional Hopf bifurcation, and the dynamics of the proposed model are influenced by selective non-linear harvesting. Furthermore, the investigation focuses on the impact of the predator's pace of harvesting about the complexities of the prey-predator relationship. Through the use of certain setting values, empirical evidence indicates as the non-integer order framework displays stable to unstable, when the non-integer order is increased. The analytical findings are shown by various instances presented in the numerical part.

Dynamical behaviors of autonomous and nonautonomous models of generalist predator–prey system with fear, mutual interference and nonlinear harvesting

In this study, we explore a predator–prey model to evaluate the impacts of fear, mutual interference, and harvesting, as these factors play crucial roles in modifying population dynamics, trophic cascades, and species interactions. Additionally, we enhance the model to incorporate the seasonality of specific ecological factors across time. The autonomous and associated nonautonomous models have undergone thorough mathematical analysis and extensive numerical simulations in the course of the study. We conduct a fundamental differential sensitivity analysis to discern the key parameters influencing both prey and predator populations within the ecosystem. Through numerical investigations of the autonomous model, we notice that in the presence (absence) of harvesting, the mutual interference among predators destabilizes (stabilizes) the coexisting equilibrium. The fear effect significantly reduces the densities of prey and predator populations, and destabilizes the coexisting equilibrium by producing multiple stability switches. The survival of predators substantially depends on the focal prey if their growth from other food sources is relatively low. Notably, the harvesting of predators is beneficial and promotes the coexistence of species only when their growth from other food sources is too much. Moreover, the system shows bistability, tristability, and multiple limit cycles under identical ecological conditions. We also show various phenomena that manifest within the seasonally forced model, including the emergence of periodic solutions, higher periodic solutions, bursting patterns, and chaotic dynamics. Remarkably, the influence of seasonal forcing possesses the capability to govern the chaotic dynamics by giving rise to an exceedingly quasi-periodic arrangement in the prey and predator densities.

Complex dynamics of a four-species food web model with nonlinear top predator harvesting and fear effect

In this paper, a four-species food web model is formulated to investigate the influence of fear effect and nonlinear top predator harvesting on the dynamical behaviors. The global stability of the system at the interior equilibrium is explored by Li–Muldowney geometric approach. By applying the Sotomayor’s theorem, it is shown that the system undergoes transcritical bifurcation and pitchfork bifurcation. The conditions for the occurrence of Hopf bifurcation are established, and the stability of the bifurcating limit cycle is discussed by normal form theory. Finally, the numerical simulations are carried out. It is observed that the system presents chaotic dynamics, periodic window and chaotic attractors. Two distinct routes to chaos are discovered, one is period doubling cascade and the other is the generation and destruction of quasi-periodic states. Moreover, it is found that the fear effect can suppress fluctuations in population density to stabilize the system.

Non Orthogonal Multiple Access (NOMA) Using a Nonlinear Energy Harvesting Model

This paper derives and optimizes the throughput of NOMA with nonlinear energy harvesting. The Base Station (BS) harvests energy from the received Radio Frequency signal. Then, the BS uses the nonlinear harvested power to diffuse packets to N users. We suggest to optimize harvesting time and the powers of users to optimize the data rate. The optimization of NOMA powers and the harvesting process were not yet performed with a non linear energy harvesting model. The study is performed for Rayleigh channels in the presence of nonlinear energy harvesting model. Furthermore, the theoretical results were confirmed using MATLAB computer simulations.

Impact of time delay in a plankton–fish system with nonlinear harvesting and external toxicity

In this study, we explore the dynamics of a plankton–fish system in which external toxic substances have adverse impacts on the plankton populations as well as the fish communities. Fish population is assumed to grow in a logistic fashion due to food sources other than zooplankton, and is being harvested at a nonlinear rate. Mathematically, we analyze the system for the feasibility and stability of the ecologically meaningful equilibria. We also obtain criteria for the optimal harvesting policy of the fishery resources. We modify the considered model to encapsulate the effect of negative feedback time delay involved in the growth of the fish population. By considering this time delay as a bifurcation parameter, we derive conditions for the existence of Hopf bifurcation; direction and stability of the bifurcating periodic solutions are also discussed. Extensive numerical simulations are done for the systems with and without time delay. The environmental toxins are found to affect the equilibrium abundances of plankton and fish population in the aquatic system. In the absence of time delay, we observe that the growths in fish population due to uptake of zooplankton and other food sources have potential to suppress the chaotic disorder and bring forth stability in the ecosystem. On the other hand, the excessive growth of phytoplankton due to overloading of nutrients and the increasing carrying capacity of the ecosystem for the fish population are found to exhibit destabilizing roles on the system’s dynamics. Finally, we observe that the larger magnitude of negative feedback time delay in the growth of fish population drives the system to a chaotic zone.