Comparison Between Different Growth Functions of the Jatropha Curcas Plant with Random Attack Pattern of Whitefly

2021 ◽  
Vol 24 (4) ◽  
pp. 382-390
Author(s):  
Roshmi Das ◽  
Ashis Kumar Sarkar
Keyword(s):  
Growth Rate ◽  
Jatropha Curcas ◽  
Stable State ◽  
Stable Limit Cycle ◽  
Stable Limit ◽  
Deterministic Models ◽  
Growth Functions ◽  
Attack Pattern ◽  
Parameter Values ◽  
Globally Stable

We have proposed here two deterministic models of Jatropha Curcas plant and Whitefly that simulate the dynamics of interaction between them where the distribution of Whitefly on plant follows Poisson distribution.In the first model growth rate of the plant is assumed to be in logistic form whereas in the second model it is taken as exponential form. The attack pattern and the growth of the whitefly are assumed as Holling type II function.The first model results a globally stable state and in the second one we find a globally attracting steady state for some parameter values,and a stable limit cycle for some other parameter values. It is also shown that there exist Hopf bifurcation with respect to some parameter values. The paper also discusses the question about persistence and permanence of the model. It is found that the specific growth rate of both the population and attack pattern of the whitefly governs the dynamics of both the models.

GLOBAL DYNAMICS AND CONTROLLABILITY OF A HARVESTED PREY-PREDATOR SYSTEM

2001 ◽  
Vol 09 (01) ◽  
pp. 67-79 ◽  
Author(s):  
P. D. N. SRINIVASU ◽  
SHAIK ISMAIL ◽  
CH. RAGHAVENDRA NAIDU
Keyword(s):  
Limit Cycle ◽  
Mathematical Analysis ◽  
Stable Limit Cycle ◽  
Global Dynamics ◽  
Stable Limit ◽  
Cyclic Behaviour ◽  
Predator Model ◽  
Globally Stable ◽  
Predator System

In this paper we have considered a prey-predator model with Holling type of predation and independent harvesting in either species. The purpose of the work is to offer mathematical analysis of the model and to discuss some significant qualitative results that are expected to arise from the interplay of biological forces. Our study shows that, using the harvesting efforts as controls, it is possible to break the cyclic behaviour of the system and drive it to a required state. Also it is possible to introduce globally stable limit cycle in the system using the above controls.

Periodicities of cardiac mechanics

1991 ◽  
Vol 261 (2) ◽  
pp. H424-H433
Author(s):  
S. A. Ben-Haim ◽  
G. Fruchter ◽  
G. Hayam ◽  
Y. Edoute
Keyword(s):  
Experimental Studies ◽  
Stable Limit Cycle ◽  
Cardiac Mechanics ◽  
Left Ventricular ◽  
Stable Limit ◽  
End Diastolic Volume ◽  
Model Predictions ◽  
Parameter Values ◽  
Theoretical Simulations ◽  
Working Heart

Using a finite-difference equation to model cardiac mechanics, we simulated the stable action of the left ventricle. This model describes the left ventricular end-diastolic volume as a function of the previous end-diastolic volume and several physiological parameters describing the mechanical properties and hemodynamic loading conditions of the heart. Our theoretical simulations demonstrated that transitions (bifurcations) can occur between different modes of dynamic organization of the isolated working heart as parameters are changed. Different regions in the parameter space are characterized by different stable limit cycle periodicities. Experimental studies carried out in an isolated working rat heart model verified the model predictions. The experimental studies showed that stable periodicities were invoked by changing the parameter values in the direction suggested by the theoretical analysis. We propose in the present work that mechanical periodicities of the heart action are an inherent part of its nonlinear nature. The model predictions and experimental results are compatible with previous experimental data but may contradict several hypotheses suggested to explain the phenomenon of cardiac periodicities.

Fragility in Dynamic Networks: Application to Neural Networks in the Epileptic Cortex

2014 ◽  
Vol 26 (10) ◽  
pp. 2294-2327 ◽  
Author(s):  
Duluxan Sritharan ◽  
Sridevi V. Sarma
Keyword(s):  
Neural Network ◽  
Structural Changes ◽  
Minimum Energy ◽  
Dynamic Networks ◽  
Structural Connectivity ◽  
Stable State ◽  
Stable Limit Cycle ◽  
State Feedback Control ◽  
Stable Limit ◽  
Small Stimulus

Epilepsy is a network phenomenon characterized by atypical activity at the neuronal and population levels during seizures, including tonic spiking, increased heterogeneity in spiking rates, and synchronization. The etiology of epilepsy is unclear, but a common theme among proposed mechanisms is that structural connectivity between neurons is altered. It is hypothesized that epilepsy arises not from random changes in connectivity, but from specific structural changes to the most fragile nodes or neurons in the network. In this letter, the minimum energy perturbation on functional connectivity required to destabilize linear networks is derived. Perturbation results are then applied to a probabilistic nonlinear neural network model that operates at a stable fixed point. That is, if a small stimulus is applied to the network, the activation probabilities of each neuron respond transiently but eventually recover to their baseline values. When the perturbed network is destabilized, the activation probabilities shift to larger or smaller values or oscillate when a small stimulus is applied. Finally, the structural modifications to the neural network that achieve the functional perturbation are derived. Simulations of the unperturbed and perturbed networks qualitatively reflect neuronal activity observed in epilepsy patients, suggesting that the changes in network dynamics due to destabilizing perturbations, including the emergence of an unstable manifold or a stable limit cycle, may be indicative of neuronal or population dynamics during seizure. That is, the epileptic cortex is always on the brink of instability and minute changes in the synaptic weights associated with the most fragile node can suddenly destabilize the network to cause seizures. Finally, the theory developed here and its interpretation of epileptic networks enables the design of a straightforward feedback controller that first detects when the network has destabilized and then applies linear state feedback control to steer the network back to its stable state.

Dynamics of a delayed competitive system affected by toxic substances with imprecise biological parameters

Filomat ◽  
2017 ◽  
Vol 31 (16) ◽  
pp. 5271-5293
Author(s):  
A.K. Pal ◽  
P. Dolai ◽  
G.P. Samanta
Keyword(s):  
Equilibrium Points ◽  
Stable Limit Cycle ◽  
Limit Cycle Oscillation ◽  
Toxic Substances ◽  
Stable Limit ◽  
Biological Parameters ◽  
Delay Model ◽  
Competitive System ◽  
Interval Numbers ◽  
Cycle Oscillation

In this paper we have studied the dynamical behaviours of a delayed two-species competitive system affected by toxicant with imprecise biological parameters. We have proposed a method to handle these imprecise parameters by using parametric form of interval numbers. We have discussed the existence of various equilibrium points and stability of the system at these equilibrium points. In case of toxic stimulatory system, the delay model exhibits a stable limit cycle oscillation. Computer simulations are carried out to illustrate our analytical findings.

MODELING THE TRANSMISSION DYNAMICS OF DAIRY CATTLE BRUCELLOSIS IN JILIN PROVINCE, CHINA

2014 ◽  
Vol 22 (04) ◽  
pp. 533-554 ◽  
Author(s):  
JING NIE ◽  
GUI-QUAN SUN ◽  
XIANG-DONG SUN ◽  
JUAN ZHANG ◽  
NAN WANG ◽  
...  
Keyword(s):  
Dairy Cattle ◽  
Rapid Development ◽  
Real Data ◽  
Jilin Province ◽  
Annual Number ◽  
Bacterial Disease ◽  
Increasing Trend ◽  
Milk Cows ◽  
Parameter Values ◽  
Globally Stable

Dairy cattle brucellosis is a chronic bacterial disease, which is caused by Brucella abortus and mainly characterized by abortion in dairy cattle. With the rapid development of breeding industry of milk cows in China, the infectious cases of dairy cattle brucellosis show an increasing trend. Particularly in Jilin province, the annual number of the positive cases of dairy cattle was only 3 cows in 1987, and went up to 168 cows in 2005. Based on the situation of the brucellosis infection in Jilin province, we propose an Susceptible-Exposed-Infected-Virus (SEIV) dynamical model with outside transferred amount to describe the transmission of brucellosis amongst dairy cattle in this paper. We calculate the basic reproduction number R0 and prove that the equilibria are globally stable. Moreover, using the real data of nearly 20 years in Jilin province, we estimate the parameter values in the system. As a result, we can predict the number of infections as time increases. According to the prediction for the next 30 years, we can conclude that the disease will persist if we just take existing measures. If culling, sterilizing and decreasing the number of outer importing are used together, dairy cattle brucellosis will be well controlled.

scholarly journals STUDYING THE STABILITY BY USING LOCAL LINEARIZATION METHOD

2020 ◽  
Vol 2 (1) ◽  
pp. 27-31
Author(s):  
Abdulghafoor Jasim Salim ◽  
Kais Ismail Ebrahem ◽  
Suhirman
Keyword(s):  
Singular Point ◽  
Limit Cycle ◽  
Autoregressive Model ◽  
Stable Limit Cycle ◽  
Linearization Method ◽  
Stable Limit ◽  
Local Linearization ◽  
Non Linear ◽  
The Stability ◽  
Local Linearization Method

Abstract: In this paper we study the stability of one of a non linear autoregressive model with trigonometric term  by using local linearization method proposed by Tuhro Ozaki .We find the singular point ,the stability of the singular point and the limit cycle. We conclude  that the proposed model under certain conditions have a non-zero singular point which is  a asymptotically salable ( when  0 ) and have an  orbitaly stable limit cycle . Also we give some examples in order to explain the method. Key Words : Non-linear Autoregressive model; Limit cycle; singular point; Stability.

scholarly journals Méthode d'agrégation des variables appliquée à la dynamique des populations

2006 ◽  
Vol Volume 5, Special Issue TAM... ◽  
Author(s):  
Pierre Auger ◽  
Abderrahim El Abdllaoui ◽  
Rachid Mchich
Keyword(s):  
Stable Limit Cycle ◽  
Stable Limit ◽  
Dynamique Des Populations ◽  
Globally Asymptotically Stable ◽  
Density Dependent ◽  
Migration Rates ◽  
First Case ◽  
International Audience ◽  
Predator Model ◽  
Predator System

International audience We present the method of aggregation of variables in the case of ordinary differential equations. We apply the method to a prey - predator model in a multi - patchy environment. In this model, preys can go to a refuge and therefore escape to predation. The predator must return regularly to his terrier to feed his progeny. We study the effect of density-dependent migration on the global stability of the prey-predator system. We consider constant migration rates, but also density-dependent migration rates. We prove that the positif equilibrium is globally asymptotically stable in the first case, and that its stability changes in the second case. The fact that we consider density-dependent migration rates leads to the existence of a stable limit cycle via a Hopf bifurcation. Nous présentons les grandes lignes de laméthode d'agrégation des variables dans les systèmes d'équations différentielles ordinaires. Nous appliquons laméthode à un modèle proie-prédateur spatialisé. Dans ce modèle, les proies peuvent échapper à la prédation en se réfugiant sur un site. Le prédateur doit aussi retourner régulièrement dans son terrier pour nourrir sa progéniture. Nous étudions les effets de migration dépendant de la densité des populations sur la stabilité globale du système proie-prédateur. Nous considérons des taux de migration constants, puis densité-dépendants. Dans le cas de taux constants il existe un équilibre positif toujours stable alors que dans le cas de taux de migration densité-dépendants, il existe un cycle limite stable via une bifurcation de Hopf.

scholarly journals Predicting Experimental Sepsis Survival with a Mathematical Model of Acute Inflammation

2021 ◽  
Vol 1 ◽  
Author(s):  
Jared Barber ◽  
Amy Carpenter ◽  
Allison Torsey ◽  
Tyler Borgard ◽  
Rami A. Namas ◽  
...  
Keyword(s):  
Immune Response ◽  
Growth Rate ◽  
Inflammatory Response ◽  
Inflammatory Responses ◽  
Initial Conditions ◽  
Mortality Data ◽  
Experimental Sepsis ◽  
Initial Inoculum ◽  
Molecular Pattern ◽  
Parameter Values

Sepsis is characterized by an overactive, dysregulated inflammatory response that drives organ dysfunction and often results in death. Mathematical modeling has emerged as an essential tool for understanding the underlying complex biological processes. A system of four ordinary differential equations (ODEs) was developed to simulate the dynamics of bacteria, the pro- and anti-inflammatory responses, and tissue damage (whose molecular correlate is damage-associated molecular pattern [DAMP] molecules and which integrates inputs from the other variables, feeds back to drive further inflammation, and serves as a proxy for whole-organism health status). The ODE model was calibrated to experimental data from E. coli infection in genetically identical rats and was validated with mortality data for these animals. The model demonstrated recovery, aseptic death, or septic death outcomes for a simulated infection while varying the initial inoculum, pathogen growth rate, strength of the local immune response, and activation of the pro-inflammatory response in the system. In general, more septic outcomes were encountered when the initial inoculum of bacteria was increased, the pathogen growth rate was increased, or the host immune response was decreased. The model demonstrated that small changes in parameter values, such as those governing the pathogen or the immune response, could explain the experimentally observed variability in mortality rates among septic rats. A local sensitivity analysis was conducted to understand the magnitude of such parameter effects on system dynamics. Despite successful predictions of mortality, simulated trajectories of bacteria, inflammatory responses, and damage were closely clustered during the initial stages of infection, suggesting that uncertainty in initial conditions could lead to difficulty in predicting outcomes of sepsis by using inflammation biomarker levels.

scholarly journals The effect of sludge retention time (SRT) on the Nitrifier typical kinetics at ambient temperature under the low ammonia density

2021 ◽  
Author(s):  
Yifan Li ◽  
Jinzhu Wu ◽  
Yongjie Liu ◽  
Feiyong Chen ◽  
Jie Guan ◽  
...  
Keyword(s):  
Growth Rate ◽  
Ambient Temperature ◽  
Retention Time ◽  
Stable State ◽  
Species Structure ◽  
Maximum Reaction Rate ◽  
Sludge Retention Time ◽  
Structure Changes ◽  
Nitrification Process ◽  
D 20

Abstract Sludge retention time (SRT) regulation is one of the essential management techniques for refined control of the main-sidestream treatment process under the low ammonia density. It is indispensable to understand the effect of SRTs changes on the Nitrifier kinetics to obtain the functional separation of the Nitrifier and the refined control of the nitrification process. In this study, Nitrifier was cultured with conditions of 35 ± 0.5 °C, pH 7.5 ± 0.2, DO 5.0 ± 0.5 mg-O/L, and SRTs was controlled for 40 d, 20 d, 10 d, and 5 d. The net growth rate (), decay rate (), specific growth rate (), the yield of the Nitrifier (), temperature parameter (), and inhibition coefficient () have been measured and extended with the SRT decreases. Instead, the half-saturation coefficient () decreased. In addition, the limited value of pH inhibition occurs (), and the pH of keeping 5% maximum reaction rate () was in a relatively stable state. The trade of kinetics may be induced by the species structure of Nitrifier changed. The Nitrosomonas proportion was increased, and the Nitrospira used to be contrary with the SRT decreasing. It is a match for the functional separation of Nitrifier when SRTs was 20 d at ambient temperature under the low ammonia density. The kinetics of ammonia-oxidizing organism (AOO) and nitrite-oxidizing organism (NOO) in Nitrifier under different SRT conditions should be measured respectively to the refined control of the partial nitrification process in the future study. HIGHLIGHT The Nitrifier typical kinetics used to be affected notably by way of SRTs changes. The species structure of the Nitrifier was recognized beneath distinctive SRTs. The change of Nitrifier kinetics with SRTs used to be estimated by the species structure changes.

Bifurcation of Codimension 3 in a Predator–Prey System of Leslie Type with Simplified Holling Type IV Functional Response

2016 ◽  
Vol 26 (02) ◽  
pp. 1650034 ◽  
Author(s):  
Jicai Huang ◽  
Xiaojing Xia ◽  
Xinan Zhang ◽  
Shigui Ruan
Keyword(s):  
Functional Response ◽  
Limit Cycle ◽  
Stable Limit Cycle ◽  
Positive Equilibrium ◽  
Stable Limit ◽  
Homoclinic Loop ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Type Iv ◽  
Stable Equilibria

It was shown in [Li & Xiao, 2007] that in a predator–prey model of Leslie type with simplified Holling type IV functional response some complex bifurcations can occur simultaneously for some values of parameters, such as codimension 1 subcritical Hopf bifurcation and codimension 2 Bogdanov–Takens bifurcation. In this paper, we show that for the same model there exists a unique degenerate positive equilibrium which is a degenerate Bogdanov–Takens singularity (focus case) of codimension 3 for other values of parameters. We prove that the model exhibits degenerate focus type Bogdanov–Takens bifurcation of codimension 3 around the unique degenerate positive equilibrium. Numerical simulations, including the coexistence of three hyperbolic positive equilibria, two limit cycles, bistability states (one stable equilibrium and one stable limit cycle, or two stable equilibria), tristability states (two stable equilibria and one stable limit cycle), a stable limit cycle enclosing a homoclinic loop, a homoclinic loop enclosing an unstable limit cycle, or a stable limit cycle enclosing three unstable hyperbolic positive equilibria for various parameter values, confirm the theoretical results.

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