Bifurcation in Plant-Pest-Natural Enemy Interaction Dynamics with Gestation Delay for Both Pest and Natural Enemy

2019 ◽  
Vol 29 (13) ◽  
pp. 1950178
Author(s):  
Vijay Kumar ◽  
Joydip Dhar ◽  
Harbax Singh Bhatti
Keyword(s):  
Natural Enemy ◽  
Equilibrium Points ◽  
Model Parameters ◽  
Natural Control ◽  
Control Approach ◽  
Gestation Delay ◽  
Interior Equilibrium ◽  
Interaction Dynamics ◽  
Plant Pest ◽  
Different Levels

During this analysis, as per natural control approach in pest management, a plant-pest dynamics with biological control is proposed, here assuming that the pest and natural enemy are having different levels of gestation delay and harvesting rate of pests by natural enemy follows Holling type-III response function. Boundedness and positivity of the system are studied. Equilibria and stability analysis is carried out for possible equilibrium points. The existence of Hopf bifurcation at interior equilibrium is presented. The sensitivity analysis of the system at interior equilibrium point for model parameters has been explored. Numerical simulations are performed to support our analytic findings.

The Model of the Integrated Control of Plant Pests with Natural Enemy

2013 ◽  
Vol 864-867 ◽  
pp. 2522-2527
Author(s):  
Xu Ying Lv ◽  
Tian Wen Yao ◽  
Ding Jiang Wang
Keyword(s):  
Biological Control ◽  
Natural Enemy ◽  
Integrated Control ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Plant Pests ◽  
First Approximation ◽  
Plant Pest ◽  
The Stability ◽  
Hurwitz Theorem

This paper mainly indicates the pest-control problem by using the biological control and the pesticide control. Firstly, it analyzed the continuous changing population of the three species-plants, plant pest and natural enemy-and the pesticides’ effects to establish a three-species model of the pests’ integrated control. Secondly, the pest equilibrium points with the natural enemy and that without natural enemy were obtained. We discussed the stability of the equilibrium points by the Hurwitz theorem and the first approximation method of stability and got the sufficient conditions for asymptotic stability. Finally, numerical simulations were performed by Matlab to analyze and verify the integrated control of plant pests in the situations with some natural enemies and without enemy. Moreover, the effects of spraying pesticides which have different killing rates on enemy and plant pest were analyzed.

scholarly journals Mathematical analysis of a measles transmission dynamics model in Bangladesh with double dose vaccination

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Md Abdul Kuddus ◽  
M. Mohiuddin ◽  
Azizur Rahman
Keyword(s):  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Transmission Rate ◽  
Equilibrium Points ◽  
Rank Correlation ◽  
Dynamical Analysis ◽  
Model Parameters ◽  
Progression Rate ◽  
Double Dose ◽  
The Basic Reproduction Number

AbstractAlthough the availability of the measles vaccine, it is still epidemic in many countries globally, including Bangladesh. Eradication of measles needs to keep the basic reproduction number less than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}<1)$$ ( i . e . R 0 < 1 ) . This paper investigates a modified (SVEIR) measles compartmental model with double dose vaccination in Bangladesh to simulate the measles prevalence. We perform a dynamical analysis of the resulting system and find that the model contains two equilibrium points: a disease-free equilibrium and an endemic equilibrium. The disease will be died out if the basic reproduction number is less than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{ R}}_{0}<1)$$ ( i . e . R 0 < 1 ) , and if greater than one $$(\mathrm{i}.\mathrm{e}. \, \, {\mathrm{R}}_{0}>1)$$ ( i . e . R 0 > 1 ) epidemic occurs. While using the Routh-Hurwitz criteria, the equilibria are found to be locally asymptotically stable under the former condition on $${\mathrm{R}}_{0}$$ R 0 . The partial rank correlation coefficients (PRCCs), a global sensitivity analysis method is used to compute $${\mathrm{R}}_{0}$$ R 0 and measles prevalence $$\left({\mathrm{I}}^{*}\right)$$ I ∗ with respect to the estimated and fitted model parameters. We found that the transmission rate $$(\upbeta )$$ ( β ) had the most significant influence on measles prevalence. Numerical simulations were carried out to commissions our analytical outcomes. These findings show that how progression rate, transmission rate and double dose vaccination rate affect the dynamics of measles prevalence. The information that we generate from this study may help government and public health professionals in making strategies to deal with the omissions of a measles outbreak and thus control and prevent an epidemic in Bangladesh.

scholarly journals On the ship course-keeping control system design by using robust feedback linearization

2013 ◽  
Vol 20 (1) ◽  
pp. 70-76 ◽  
Author(s):  
Zenon Zwierzewicz
Keyword(s):  
Feedback Linearization ◽  
High Performance ◽  
Linearization Method ◽  
Model Parameters ◽  
Control System Design ◽  
Control Approach ◽  
Ship Model ◽  
Control Techniques ◽  
System Nonlinearity ◽  
Ship Autopilot

Abstract In the paper the problem of ship autopilot design based on feedback linearization method combined with the robust control approach, is considered. At first the nonlinear ship model (of Norrbin type) is linearized with the use of the simple system nonlinearity cancellation. Next, bearing in mind that exact values of the model parameters are not known, the ensuing inaccuracies are taken as disturbances acting on the system. Thereby is obtained a linear system with an extra term representing the uncertainty which can be treated by using robust, H∞ optimal control techniques. The performed simulations of ship course-changing process confirmed a high performance of the proposed controller despite the assumed significant errors of its parameters.

scholarly journals Dynamical Behaviour in Two Prey-Predator System with Persistence

2016 ◽  
Vol 16 ◽  
pp. 20-37
Author(s):  
V. Madhusudanan ◽  
S. Vijaya
Keyword(s):  
Limit Cycle ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Dynamical Behaviour ◽  
Positive Equilibrium ◽  
Predator Population ◽  
Interior Equilibrium ◽  
Trivial Equilibrium ◽  
Necessary And Sufficient

In this work, the dynamical behavior of the system with two preys and one predator population is investigated. The predator exhibits a Holling type II response to one prey which is harvested and a Beddington-DeAngelis functional response to the other prey. The boundedness of the system is analyzed. We examine the occurrence of positive equilibrium points and stability of the system at those points. At trivial equilibrium E0and axial equilibrium (E1); the system is found to be unstable. Also we obtain the necessary and sufficient conditions for existence of interior equilibrium point (E6) and local and global stability of the system at the interior equilibrium (E6): Depending upon the existence of limit cycle, the persistence condition is established for the system. The numerical simulation infer that varying the parameters such as e and λ1it is possible to change the dynamical behavior of the system from limit cycle to stable spiral. It is also observed that the harvesting rate plays a crucial role in stabilizing the system.

scholarly journals Three-dimensional data-tracking simulations of sprinting using a direct collocation optimal control approach

PeerJ ◽  
2021 ◽  
Vol 9 ◽  
pp. e10975
Author(s):  
Nicos Haralabidis ◽  
Gil Serrancolí ◽  
Steffi Colyer ◽  
Ian Bezodis ◽  
Aki Salo ◽  
...  
Keyword(s):  
Experimental Data ◽  
Reaction Force ◽  
Three Dimensional ◽  
Contact Model ◽  
Model Parameters ◽  
Ground Contact ◽  
Control Approach ◽  
Average Percentage ◽  
Data Tracking ◽  
The Individual

Biomechanical simulation and modelling approaches have the possibility to make a meaningful impact within applied sports settings, such as sprinting. However, for this to be realised, such approaches must first undergo a thorough quantitative evaluation against experimental data. We developed a musculoskeletal modelling and simulation framework for sprinting, with the objective to evaluate its ability to reproduce experimental kinematics and kinetics data for different sprinting phases. This was achieved by performing a series of data-tracking calibration (individual and simultaneous) and validation simulations, that also featured the generation of dynamically consistent simulated outputs and the determination of foot-ground contact model parameters. The simulated values from the calibration simulations were found to be in close agreement with the corresponding experimental data, particularly for the kinematics (average root mean squared differences (RMSDs) less than 1.0° and 0.2 cm for the rotational and translational kinematics, respectively) and ground reaction force (highest average percentage RMSD of 8.1%). Minimal differences in tracking performance were observed when concurrently determining the foot-ground contact model parameters from each of the individual or simultaneous calibration simulations. The validation simulation yielded results that were comparable (RMSDs less than 1.0° and 0.3 cm for the rotational and translational kinematics, respectively) to those obtained from the calibration simulations. This study demonstrated the suitability of the proposed framework for performing future predictive simulations of sprinting, and gives confidence in its use to assess the cause-effect relationships of technique modification in relation to performance. Furthermore, this is the first study to provide dynamically consistent three-dimensional muscle-driven simulations of sprinting across different phases.

Fear Induced Stabilization in an Intraguild Predation Model

2020 ◽  
Vol 30 (04) ◽  
pp. 2050053
Author(s):  
Mainul Hossain ◽  
Nikhil Pal ◽  
Sudip Samanta ◽  
Joydev Chattopadhyay
Keyword(s):  
Growth Rate ◽  
Hopf Bifurcation ◽  
Intraguild Predation ◽  
Equilibrium Points ◽  
Stable Limit ◽  
Interior Equilibrium ◽  
The Rich ◽  
The Stability ◽  
The Cost ◽  
The Impact

In the present paper, we investigate the impact of fear in an intraguild predation model. We consider that the growth rate of intraguild prey (IG prey) is reduced due to the cost of fear of intraguild predator (IG predator), and the growth rate of basal prey is suppressed due to the cost of fear of both the IG prey and the IG predator. The basic mathematical results such as positively invariant space, boundedness of the solutions, persistence of the system have been investigated. We further analyze the existence and local stability of the biologically feasible equilibrium points, and also study the Hopf-bifurcation analysis of the system with respect to the fear parameter. The direction of Hopf-bifurcation and the stability properties of the periodic solutions have also been investigated. We observe that in the absence of fear, omnivory produces chaos in a three-species food chain system. However, fear can stabilize the chaos thus obtained. We also observe that the system shows bistability behavior between IG prey free equilibrium and IG predator free equilibrium, and bistability between IG prey free equilibrium and interior equilibrium. Furthermore, we observe that for a suitable set of parameter values, the system may exhibit multiple stable limit cycles. We perform extensive numerical simulations to explore the rich dynamics of a simple intraguild predation model with fear effect.

Impact of Additive Allee Effect on the Dynamics of an Intraguild Predation Model with Specialist Predator

2020 ◽  
Vol 30 (16) ◽  
pp. 2050239
Author(s):  
Udai Kumar ◽  
Partha Sarathi Mandal
Keyword(s):  
System Dynamics ◽  
Equilibrium Point ◽  
Intraguild Predation ◽  
Allee Effect ◽  
Equilibrium Points ◽  
Dimensional System ◽  
Global Dynamics ◽  
Interior Equilibrium ◽  
Trivial Equilibrium ◽  
The Impact

Many important factors in ecological communities are related to the interplay between predation and competition. Intraguild predation or IGP is a mixture of predation and competition which is a very basic three-dimensional system in food webs where two species are related to predator–prey relationship and are also competing for a shared prey. On the other hand, Allee effect is also a very important ecological factor which causes significant changes to the system dynamics. In this work, we consider a intraguild predation model in which predator is specialist, the growth of shared prey population is subjected to additive Allee effect and there is Holling-Type III functional response between IG prey and IG predator. We analyze the impact of Allee effect on the global dynamics of the system with the prior knowledge of the dynamics of the model without Allee effect. Our theoretical and numerical analyses suggest that: (1) Trivial equilibrium point is always locally asymptotically stable and it may be globally stable also. Hence, all the populations may go to extinction depending upon initial conditions; (2) Bistability is observed between unique interior equilibrium point and trivial equilibrium point or between boundary equilibrium point and trivial equilibrium point; (3) Multiple interior equilibrium points exist under certain parameters range. We also provide here a comprehensive study of bifurcation analysis by considering Allee effect as one of the bifurcation parameters. We observed that Allee effect can generate all possible bifurcations such as transcritical bifurcation, saddle-node bifurcation, Hopf bifurcation, Bogdanov–Taken bifurcation and Bautin bifurcation. Finally, we compared our model with the IGP model without Allee effect for better understanding the impact of Allee effect on the system dynamics.

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