Spruce Budworm Model Research Articles

When do multiple pulses of environmental variation trigger tipping in an ecological system?

Climate change and anthropogenic impacts have a significant effect on natural ecosystems. As a response, tipping phenomena, i.e., abrupt qualitative changes in the dynamics of ecosystems, like transitions between alternative stable states, can be observed. We study such critical transitions, caused by an interplay between B-tipping, the rate of change of environmental forcing, and a rate-dependent basin boundary crossing. Instead of a slow trend of environmental change, we focus on pulses of variation in the carrying capacity in a simple ecological model, the spruce budworm model, and show how one pulse of environmental change can lead to tracking the current stable state or to tipping to an alternative state depending on the strength and the duration of the pulse. Moreover, we demonstrate that applying a second pulse after the first one, which can track the desired state, can lead to tipping, although its rate is slow and does not even cross the critical threshold. We explain this unexpected behavior in terms of the interacting timescales, the intrinsic ecological timescale, the rate of environmental change, and the movement of the basin boundaries separating the basins of attraction of the two alternative states.

Pattern dynamics analysis of a space–time discrete spruce budworm model

In view of the living habits of the spruce budworm, a space–time discrete model with periodic boundary conditions is established. Through the analysis of the effect of diffusion, rich dynamic properties are obtained, such as chaotic phenomena, stable spatially homogeneous states, pure Turing instability, spatially homogeneous periodic oscillations, and Flip-Turing instability. These findings hold significant biological significance and offer valuable insights for research in ecosystem stability study, pest control strategies, as well as evolution and adaptation studies. In addition, the relationship between complex patterns and biological mechanisms is discussed. The results in this paper can help people better understand the biological significance of controlling the spruce budworm.

ANALYSIS OF THE SPRUCE BUDWORM MODEL USING THE HEUN METHOD AND THIRD-ORDER RUNGE-KUTTA

This study discusses the analysis of the Spruce Budworm model using numerical methods, namely the Heun method and the Third Order Runge-Kutta method. The purpose of this study is to determine the numerical results of the Heun method and the Third Order Runge-Kutta method on the cypress caterpillar model and to determine the comparison of errors from the two methods, namely the Heun method and the Third Order Runge-Kutta method in analyzing the Spruce Budworm model. The results of the study using the Heun method for the initial conditions at years, for , the result obtained is and . For the calculation result of the Spruce Budworm model using the third-order Runge-Kutta method, the result obtained is and . while the error of Caterpillar Density with the third-order Runge-Kutta method is bigger than the Heun method, while the error of Branch Surface Area and the error of Reserve Food error using the Heun method bigger than using the third-order Runge-Kutta method.

Dynamic Analysis of a Model for Spruce Budworm Populations with Delay

A class of delayed spruce budworm population model is considered. Compared with previous studies, both autonomous and nonautonomous delayed spruce budworm population models are considered. By using the inequality techniques, continuation theorem, and the construction of suitable Lyapunov functional, we establish a set of easily verifiable sufficient conditions on the permanence, existence, and global attractivity of positive periodic solutions for the considered system. Finally, an example and its numerical simulation are given to illustrate our main results.

Periodic solutions and spatial patterns induced by mixed delays in a diffusive spruce budworm model with Holling II predation function

In present article, under homogeneous Neumann boundary condition, we put forward a diffusive spruce budworm model with mixed delays and Holling II predation function firstly. Then, choosing delay (discrete delay or distributed delay) as bifurcating parameter together with characteristic equation, we derive that not only can discrete delay induce the appearance of Hopf bifurcations for this model, but also distributed delay can do it. However, to our knowledge, in the known literatures, Hopf bifurcation can only be deduced by discrete delay or distributed delay. So, the obtained results in present article are new. At last, by carrying out numerical simulations, we obtain periodic solutions and spatial patterns deduced by discrete delay or distributed delay, which illustrates the results in this article.

Dynamics of Spruce budworms and single species competition models with bifurcation analysis

Choristoneura Fumiferana is perilous defoliators of forest lands in North America and many countries in Europe. In this study, we consider mathematical models in ecology, epidemiology and bifurcation studies; the spruce budworm model and the population model with harvesting. The study is designed based on bifurcation analysis. In particular, the results support population thresholds necessary for survival in certain cases. In a series of numerical examples, the outcomes are presented graphically to compare with bifurcation results.

STABILITY AND HOPF BIFURCATION ANALYSIS ON A SPRUCE-BUDWORM MODEL WITH DELAY

In this paper, the dynamics of a spruce-budworm model with delay is investigated. We show that there exists Hopf bifurcation at the positive equilibrium as the delay increases. Some sufficient conditions for the existence of Hopf bifurcation are obtained by investigating the associated characteristic equation. By using the theory of normal form and center manifold, explicit expression for determining the direction of Hopf bifurcations and the stability of bifurcating periodic solutions are presented.

The concept of force in population dynamics

The area of population dynamics has a rich history of the development and analysis of models of biological and social phenomena using ordinary differential equations. This paper describes a method for understanding the influence one variable exerts on another in such models as a force, with the relative effects of these forces providing a narrative explanation of the curvature in variable behaviour. Using the stock/flow form of a model, a symbolic notation is developed that identifies the forces with the causal pathways of the model’s feedback loops. A force is measured by its impact, defined as the ratio of acceleration to rate of change, computed by differentiation along its associated pathway between variables. Different phases of force dominance are determined to enhance the standard stability analysis of the models, providing an explanation of model behaviour in Newtonian mechanical terms. The concepts developed are applied to well-known models from mathematical biology: the Spruce Budworm model, where force dominance identifies scenarios that give clarity to intervention points; and the Lotka–Volterra predator–prey model where the analysis highlights the importance of dissipative forces in achieving stability. Conclusions are drawn on the explanatory power of this approach, with suggestions made for future work.

Entire solutions of the spruce budworm model

This paper is concerned with the entire solutions of the spruce budworm model, i.e., solutions defined for all (x,t)in mathbb{R}^{2}. Using the comparison argument and sub-super-solution method, three types of the entire solutions are obtained, and each one of them behaves like two traveling fronts that come from both sides of the real axis and mix.

Turing-Hopf bifurcation of a class of modified Leslie-Gower model with diffusion

In this paper, the dynamics of a class of modified Leslie-Gower model with diffusion is considered. The stability of positive equilibrium and the existence of Turing-Hopf bifurcation are shown by analyzing the distribution of eigenvalues. The normal form on the centre manifold near the Turing-Hopf singularity is derived by using the method of Song et al. Finally, some numerical simulations are carried out to illustrate the analytical results. For spruce budworm model, the dynamics in the neighbourhood of the bifurcation point can be divided into six categories, each of which is exactly demonstrated by the numerical simulations. Then according to this dynamical classification, a stable spatially inhomogeneous periodic solution has been found, which can be used to explain the phenomenon of periodic outbreaks of spruce budworm.

Numerical existence and stability of solutions to the distributed spruce budworm model

This paper presents the steady-state solutions and traveling wave solutions for a spatially distributed PDE version of the spruce budworm model. The ODE (undistributed) model has been used in practical scenarios to model the outbreaks of the spruce budworm in forest environments, alongside the study of concepts involving fixed points and bifurcations in introductory differential equations courses. This study represents the spread of an outbreak from one end of a forest to the other. Numerical simulations are conducted using spectral methods.

Bifurcation analysis of a spruce budworm model with diffusion and physiological structures

In this paper, the dynamics of a spruce budworm model with diffusion and physiological structures are investigated. The stability of steady state and the existence of Hopf bifurcation near positive steady state are investigated by analyzing the distribution of eigenvalues. The properties of Hopf bifurcation are determined by the normal form theory and center manifold reduction for partial functional differential equations. And global existence of periodic solutions is established by using the global Hopf bifurcation result of Wu. Finally, some numerical simulations are carried out to illustrate the analytical results.

Slow-fast dynamics of Hopfield spruce-budworm model with memory effects

In this paper we consider a kind of the spruce-budworm system with memory effects. On the basis of geometric singular perturbation theory, the transition of the solution trajectory is illustrated, and the existence of the relaxation oscillation with a rapid movement process alternating with a slow movement process is proved. The characteristic of the relaxation oscillation, it is indicated, is dependent on the structure of the slow manifold. Moreover, the approximate expression of the relaxation oscillation and its period are obtained analytically. Finally we present two simulations to demonstrate the validity of the analytical conclusion.

Age-dependent intra-specific competition in pre-adult life stages and its effects on adult population dynamics

Intra-specific competition in insect and amphibian species is often experienced in completely different ways in their distinct life stages. Competition among larvae is important because it can impact on adult traits that affect disease transmission, yet mathematical models often ignore larval competition. We present two models of larval competition in the form of delay differential equations for the adult population derived from age-structured models that include larval competition. We present a simple prototype equation that models larval competition in a simplistic way. Recognising that individual larvae experience competition from other larvae at various stages of development, we then derive a more complex equation containing an integral with a kernel that quantifies the competitive effect of larvae of ageāon larvae of agea. In some parameter regimes, this model and the famous spruce budworm model have similar dynamics, with the possibility of multiple co-existing equilibria. Results on boundedness and persistence are also proved.

Existence and Uniqueness of Positive Solutions of a Randomized Spruce Budworm Model

Spruce Budworm is the most destructive defoliator of coniferous forests in Western North America .This paper discusses a randomized Spruce Budworm model with HollingIII Functional Response. Using results from lyapunov function, we show that the positive solution of the associated stochastic differential equation does not explode to infinity in a finite time under simple assumption .It is shown to improve existing results.

The steady states in the Spruce Budworm model : the general case

In this paper we study the steady states and the steady domains for the Spruce Budworm model in the general case where K, r, b, p,α are arbitrary positive numbers.

A NUMERICAL STUDY OF THE SPRUCE BUDWORM REACTION‐DIFFUSION EQUATION WITH HOSTILE BOUNDARIES

ABSTRACT. One of the interesting single species reaction diffusion problems is the spruce budworm model describing insect dispersal behavior. In an earlier study, Singh et al. [7] considered the two‐dimensional spruce budworm model with density dependent diffusion balanced by an artificial wind equal to the population gradient. Here we extend the model by considering more realistic density dependent diffusion and advection with hostile boundaries. We solve this model using a splitting method in which advection, diffusion and reaction processes are separated. Various hostility conditions have been used at the boundary. The numerical results show that the population moves quickly to a steady state outbreak situation when the advective components due to the density dependent diffusion are included.

NUMERICAL STUDY OF THE TWO‐DIMENSIONAL SPRUCE BUDWORM REACTION‐DIFFUSION EQUATION WITH DENSITY DEPENDENT DIFFUSION

The spruce budworm model is one of the interesting single species reaction‐diffusion problems describing insect dispersal behavior. In this paper, we investigate a two‐dimensional model with linear diffusion dependence and a convective wind.This system has been successfully solved using an operator splitting method for various domains and initial conditions. The numerical results show that populations can grow and diffuse in such a way as to produce steady state outbreak populations or steady state inhomogeneous spatial patterns in which they aggregate with low population densities.

Optimisation du complexe récolte–pulvérisation dans la lutte contre la tordeuse des bourgeons de l'épinette

An optimization model was developed as an additional tool for the management of the forest – spruce budworm (Choristoneurafumiferana (Clem.)) complex. The management objectives being considered deal only with losses in wood and the direct benefits of wood production. The spruce budworm model developed by the Institute of Resource Ecology, University of British Columbia, was used to evaluate the results of various management strategies for the forest–budworm complex. Based on dynamic programming, the optimization model determines in a temporal frame the optimal rates of insecticide to be sprayed and the annual rhythm of forest harvesting.