Effect of Copper on the interaction between the Predator Didinium nasutum and its Prey Paramecium caudatum

1990 ◽  
Vol 47 (6) ◽  
pp. 1122-1127 ◽  
Author(s):  
Christine M. Doucet ◽  
Edward J. Maly
Keyword(s):  
Equilibrium Point ◽  
Mathematical Analysis ◽  
Copper Toxicity ◽  
Copper Stress ◽  
Paramecium Caudatum ◽  
The Stability ◽  
Effect Of Copper ◽  
Predator Efficiency

Tests to determine acute copper toxicity levels demonstrated that the protozoan predator Didinium nasutum were more susceptible to copper stress than its prey Paramecium caudatum Thus we predicted that Paramecium and Didinium densities, at the equilibrium point of their interaction, would be higher at sublethal copper levels due to a decrease in the predator's efficiency. This situation is likely to produce a decrease in the stability of the system. However, isocline analysis did not support the predictions based on the acute lethality tests. Equilibrium densities of both predator and prey did not change at copper levels between 30 and 180 μg/L. The mathematical analysis suggested that the interaction became less stable with increasing copper concentrations. However, stability decreased due to hormesis in Didinium at sublethal copper levels and not due to a reduction in predator efficiency as expected. At 300 μg Cu/L, densities of both species at equilibrium were higher and the stability of the system decreased. This decrease in stability resulted from a reduction in predator efficiency, as 300 μg Cu/L is not sublethal for Didinium.

scholarly journals Stability analysis of the coexistence equilibrium of a balanced metapopulation model

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Shodhan Rao ◽  
Nathan Muyinda ◽  
Bernard De Baets
Keyword(s):  
Equilibrium Point ◽  
Mathematical Proof ◽  
Mean Field ◽  
Patch Dynamics ◽  
System Modelling ◽  
Metapopulation Model ◽  
Ode System ◽  
Homogeneous Network ◽  
The Stability ◽  
Coexistence Equilibrium

AbstractWe analyze the stability of a unique coexistence equilibrium point of a system of ordinary differential equations (ODE system) modelling the dynamics of a metapopulation, more specifically, a set of local populations inhabiting discrete habitat patches that are connected to one another through dispersal or migration. We assume that the inter-patch migrations are detailed balanced and that the patches are identical with intra-patch dynamics governed by a mean-field ODE system with a coexistence equilibrium. By making use of an appropriate Lyapunov function coupled with LaSalle’s invariance principle, we are able to show that the coexistence equilibrium point within each patch is locally asymptotically stable if the inter-patch dispersal network is heterogeneous, whereas it is neutrally stable in the case of a homogeneous network. These results provide a mathematical proof confirming the existing numerical simulations and broaden the range of networks for which they are valid.

scholarly journals Betacyanin accumulation and guaiacol peroxidase activity in Beta vulgaris L. leaves following copper stress

2012 ◽  
Vol 81 (3) ◽  
pp. 193-201 ◽  
Author(s):  
Janet M. León Morales ◽  
Mario Rodríguez-Monroy ◽  
Gabriela Sepúlveda-Jiménez
Keyword(s):  
Lipid Peroxidation ◽  
Beta Vulgaris ◽  
Defense Responses ◽  
Hydroponic Culture ◽  
Copper Stress ◽  
Guaiacol Peroxidase ◽  
Copper Exposure ◽  
Plant Parts ◽  
Young Leaves ◽  
Effect Of Copper

The effect of copper stress on betacyanin accumulation and guaiacol peroxidase (GPOD) activity in leaves of different age was evaluated in red beet (<em>Beta vulgaris </em>L. var. Crosby Egyptian) plants. In hydroponic culture, plants were treated with 0.3 μM (control), 50 μM, 100 μM, and 250 μM of CuSO<sub>4</sub> for 6 days. Copper was taken up and accumulated in old roots but was not translocated to leaves. However in young leaves, the increase of lipid peroxidation and reduction of growth were evident from day 3 of copper exposure; whereas in old leaves, the lipid peroxidation and growth were the same from either copper-treated or control plants. In response to copper exposure, the betacyanin accumulation was evident in young leaves by day 3, and continued to increase until day 6. Betacyanin only were accumulated in old leaves until day 6, but the contents were from 4 to 5 times lower than those observed in young leaves at the same copper concentrations. GPOD activity increased 3.3- and 1.4-fold in young and old leaves from day 3 of copper treatment respectively, but only in the young leaves was sustained at the same level until day 6. Old roots shown betacyanin in the control plants, but the betacyanin level and growth were reduced with the copper exposure. In contrast, young roots emerged by copper effect also accumulated copper and showed the highest betacyanin content of all plant parts assayed. These results indicate that betacyanin accumulation and GPOD activity are defense responses to copper stress in actively growing organs.

scholarly journals Further Investigations on the Dynamics and Multistability Coexisted in a Memory-Based Cobweb Model

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
S. S. Askar
Keyword(s):  
Fixed Point ◽  
Equilibrium Point ◽  
Profit Maximization ◽  
Period Doubling ◽  
Speed Of Adjustment ◽  
Discrete Dynamic ◽  
Cobweb Model ◽  
Numerical Studies ◽  
Market Clearing Price ◽  
The Stability

Based on a nonlinear demand function and a market-clearing price, a cobweb model is introduced in this paper. A gradient mechanism that depends on the marginal profit is adopted to form the 1D discrete dynamic cobweb map. Analytical studies show that the map possesses four fixed points and only one attains the profit maximization. The stability/instability conditions for this fixed point are calculated and numerically studied. The numerical studies provide some insights about the cobweb map and confirm that this fixed point can be destabilized due to period-doubling bifurcation. The second part of the paper discusses the memory factor on the stabilization of the map’s equilibrium point. A gradient mechanism that depends on the marginal profit in the past two time steps is adopted to incorporate memory in the model. Hence, a 2D discrete dynamic map is constructed. Through theoretical and numerical investigations, we show that the equilibrium point of the 2D map becomes unstable due to two types of bifurcations that are Neimark–Sacker and flip bifurcations. Furthermore, the influence of the speed of adjustment parameter on the map’s equilibrium is analyzed via numerical experiments.

scholarly journals Mathematical Modelling of Deforestation Due to Population Density and Industrialization

Jurnal Varian ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 9-16
Author(s):  
Didiharyono D. ◽  
Irwan Kasse
Keyword(s):  
Numerical Simulation ◽  
Population Density ◽  
Mathematical Modelling ◽  
Equilibrium Point ◽  
Equilibrium Points ◽  
Stability Criteria ◽  
Hurwitz Stability ◽  
Stable Conditions ◽  
Linear Differential ◽  
The Stability

The focus of the study in this paper is to model deforestation due to population density and industrialization. To begin with, it is formulated into a mathematical modelling which is a system of non-linear differential equations. Then, analyze the stability of the system based on the Routh-Hurwitz stability criteria. Furthermore, a numerical simulation is performed to determine the shift of a system. The results of the analysis to shown that there are seven non-negative equilibrium points, which in general consist equilibrium point of disturbance-free and equilibrium points of disturbances. Equilibrium point TE7(x, y, z) analyzed to shown asymptotically stable conditions based on the Routh-Hurwitz stability criteria. The numerical simulation results show that if the stability conditions of a system have been met, the system movement always occurs around the equilibrium point.

scholarly journals APLIKASI MODEL EPIDEMIK SEIAR-SEI PADA PENYEBARAN PENYAKIT MALARIA DENGAN INFEKSI ASIMTOMATIK DAN SUPER INFEKSI

2018 ◽  
Vol 15 (2) ◽  
pp. 67
Author(s):  
Stella Maryana Belwawin
Keyword(s):  
Equilibrium Point ◽  
Basic Reproduction Number ◽  
Reproduction Number ◽  
Asymptomatic Infection ◽  
Endemic Equilibrium ◽  
Asymptomatic Infections ◽  
The Stability ◽  
Super Infection ◽  
The Basic Reproduction Number

AbstractThis aim of this study is to determine the point of equilibrium and analyze the stability of SEIAR-SEI model on malaria disease with asymptomatic infection, super infection and the effect of the mosquito's life cycle. This study also aim is to measure the sensitivity of the spread of malaria to the parameters of asymptomatic infections, the rate of treatment, and the rate of birth of mosquitoes through the magnitude of . The method in this research is deductively, through several stage, such as  determination of disease-free equilibrium point and endemic equilibrium point, determination of basic reproduction number (), analyze of the basic reproduction number sensitivity of the spread of malaria to the parameters of asymptomatic infections, the rate of treatment, and the rate of birth of mosquitoes. The endemic equilibrium point was obtained using rule of Descartes. The result show that the change in the value of parameter , , and  has effect on the basic reproduction number (). Treatment factors in the human population influence the elimination of malaria in a population. Whereas asymptomatic infection factors and the birth rate of adult mosquitoes influence the increase in malaria infection. Keywords:  Malaria, asymptomatic infection, super infection, basic reproduction number, rule of descrates. AbstrakPenelitian ini bertujuan menentukan titik keseimbangan dan menganalisis kestabilan dari model SEIAR_SEI pada penyakit malaria dengan pengaruh infeksi asimtomatik, super infeksi, dan siklus hidup nyamuk. Penelitian ini juga bertujuan mengukur tingkat sensitivitas penyebaran penyakit malaria terhadap parameter infeksi asimtomatik, laju pengobatan, serta laju kelahiran nyamuk.melalu besaran .  Metode yang digunakan dalam penelitian ini adalah metode deduktif dengan langkah-langkah : menentukan titik keseimbangan bebas penyakit dan endemik dan menentukan bilangan reproduksi dasar ). Analisis sensitivitas bilangan reproduksi dasar dilakukan terhadap parameter infeksi asimtomatik, pengobatan, dan laju kelahiran nyamuk. Tititk keseimbangan endemik diperoleh dengan aturan descrates. Hasil yang diperoleh menunjukkan parameter , , dan  berpengaruh terhadap bilangan reproduksi dasar (). Faktor pengobatan berpengaruh terhadap eliminasi penyakit malaria. Sedangkan faktor infeksi asimtomatik dan laju kelahiran nyamuk dewasa berpengaruh terhadap peningkatan infeksi penyakit malaria. Kata kunci: Malaria, Infeksi Asimtomatik, Super Infeksi, Bilangan Reproduksi Dasar, Aturan Descrates . 

ATTRACTABILITY AND LOCATION OF EQUILIBRIUM POINT OF CELLULAR NEURAL NETWORKS WITH TIME-VARYING DELAYS

2004 ◽  
Vol 14 (05) ◽  
pp. 337-345 ◽  
Author(s):  
ZHIGANG ZENG ◽  
DE-SHUANG HUANG ◽  
ZENGFU WANG
Keyword(s):  
Neural Networks ◽  
Exponential Stability ◽  
Equilibrium Point ◽  
Global Exponential Stability ◽  
Cellular Neural Networks ◽  
Stability Conditions ◽  
Time Varying ◽  
The Stability ◽  
Theoretical Results

This paper presents new theoretical results on global exponential stability of cellular neural networks with time-varying delays. The stability conditions depend on external inputs, connection weights and delays of cellular neural networks. Using these results, global exponential stability of cellular neural networks can be derived, and the estimate for location of equilibrium point can also be obtained. Finally, the simulating results demonstrate the validity and feasibility of our proposed approach.

scholarly journals Note on the Stability Property of a Cooperative System Incorporating Harvesting

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Xiangdong Xie ◽  
Fengde Chen ◽  
Yalong Xue
Keyword(s):  
Iterative Method ◽  
Equilibrium Point ◽  
Stability Property ◽  
Global Attractivity ◽  
Positive Equilibrium ◽  
Cooperative System ◽  
Cooperative Model ◽  
Interior Equilibrium ◽  
The Stability

The stability of a kind of cooperative model incorporating harvesting is revisited in this paper. By using an iterative method, the global attractivity of the interior equilibrium point of the system is investigated. We show that the condition which ensures the existence of a unique positive equilibrium is enough to ensure the global attractivity of the positive equilibrium. Our results significantly improve the corresponding results of Wei and Li (2013).

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