local stability
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2022 ◽  
Vol 172 ◽  
pp. 108858
Author(s):  
Viktor Gribniak ◽  
Arvydas Rimkus ◽  
Ieva Misiūnaitė ◽  
Tautvydas Zakaras

2022 ◽  
Author(s):  
Emine Deniz Tekin

We perform all-atom molecular dynamics simulations to study the effects of the N-linked glycans on the stability of the spike glycoprotein in SARS-CoV-2. After a 100 ns of simulation on the spike proteins without and with the N-linked glycans, we found that the presence of glycans increases the local stability in their vicinity; even though their effect on the full structure is negligible.


2022 ◽  
Vol 7 (4) ◽  
pp. 4898-4935
Author(s):  
Mamta Barik ◽  
◽  
Chetan Swarup ◽  
Teekam Singh ◽  
Sonali Habbi ◽  
...  

<abstract><p>Consistently, influenza has become a major cause of illness and mortality worldwide and it has posed a serious threat to global public health particularly among the immuno-compromised people all around the world. The development of medication to control influenza has become a major challenge now. This work proposes and analyzes a structured model based on two geographical areas, in order to study the spread of influenza. The overall underlying population is separated into two sub populations: urban and rural. This geographical distinction is required as the immunity levels are significantly higher in rural areas as compared to urban areas. Hence, this paper is a novel attempt to proposes a linear and non-linear mathematical model with adaptive immunity and compare the host immune response to disease. For both the models, disease-free equilibrium points are obtained which are locally as well as globally stable if the reproduction number is less than 1 (<italic>R</italic><sub>01</sub> &lt; 1 &amp; <italic>R</italic><sub>02</sub> &lt; 1) and the endemic point is stable if the reproduction number is greater then 1 (<italic>R</italic><sub>01</sub> &gt; 1 &amp; <italic>R</italic><sub>02</sub> &gt; 1). Next, we have incorporated two treatments in the model that constitute the effectiveness of antidots and vaccination in restraining viral creation and slow down the production of new infections and analyzed an optimal control problem. Further, we have also proposed a spatial model involving diffusion and obtained the local stability for both the models. By the use of local stability, we have derived the Turing instability condition. Finally, all the theoretical results are verified with numerical simulation using MATLAB.</p></abstract>


2022 ◽  
Vol 355 ◽  
pp. 03048
Author(s):  
Bochen Han ◽  
Shengming Yang ◽  
Guangping Zeng

In this paper, we consider a predator-prey system with two time delays, which describes a prey–predator model with parental care for predators. The local stability of the positive equilibrium is analysed. By choosing the two time delays as the bifurcation parameter, the existence of Hopf bifurcation is studied. Numerical simulations show the positive equilibrium loses its stability via the Hopf bifurcation when the time delay increases beyond a threshold.


2022 ◽  
Vol 4 (1) ◽  
pp. 50-63
Author(s):  
P. K. Santra ◽  
Hasan S. Panigoro ◽  
G. S. Mahapatra

In this paper, a discrete-time predator-prey model involving prey refuge proportional to predator density is studied. It is assumed that the rate at which prey moves to the refuge is proportional to the predator density. The fixed points, their local stability, and the existence of Neimark-Sacker bifurcation are investigated. At last, the numerical simulations consisting of bifurcation diagrams, phase portraits, and time-series are given to support analytical findings. The occurrence of chaotic solutions are also presented by showing the Lyapunov exponent while some parameters are varied.


2022 ◽  
Author(s):  
Marco A. Arteaga ◽  
Alejandro Gutiérrez-Giles ◽  
Javier Pliego-Jiménez

Author(s):  
S. Magudeeswaran ◽  
S. Vinoth ◽  
K. Sathiyanathan ◽  
M. Sivabalan

This paper deals with the investigation of the three species food-web model. This model includes two logistically growing interaction species, namely [Formula: see text] and [Formula: see text], and the third species [Formula: see text] behaves as the predator and also host for [Formula: see text]. The species [Formula: see text] predating on the species [Formula: see text] with the Holling type-II functional response, while the first species [Formula: see text] is benefited from the third species [Formula: see text]. Further, the effect of fear is incorporated in the growth rate of species [Formula: see text] due to the predator [Formula: see text] and time lag in [Formula: see text] due to the gestation process. We explore all the biologically possible equilibrium points, and their local stability is analyzed based on the sample parameters. Next, we investigate the occurrence of Hopf-bifurcation around the interior equilibrium point by taking the value of the fear parameter as a bifurcation parameter for the non-delayed system. Moreover, we verify the local stability and existence of Hopf-bifurcation for the corresponding delayed system. Also, the direction and stability of the bifurcating periodic solutions are determined using the normal form theory and the center manifold theorem. Finally, we perform extensive numerical simulations to support the evidence of our analytical findings.


2021 ◽  
Vol 8 (2) ◽  
pp. 90
Author(s):  
Idy BA ◽  
Papa Ibrahima NDIAYE ◽  
Mahe Ndao ◽  
AboubaKary Diakhaby

Limiting resource is a angular stone of the interactions between species in ecosystems such as competition, prey-predators and food chain systems. In this paper, we propose a planar system as an extension of Lotka-Voterra competition model. This describes? two competitive species for a single resource? which are affected by intra and inter-specific interference. We give its complete analysis for the existence and local stability of all equlibria and some conditions of global stability. The model exhibits a rich set of behaviors with a multiplicity of coexistence equilibria, bi-stability, tri-stability and occurrence of global stability of the exclusion of one species and the coexistence? equilibrium. The asymptotic behavior and the number of coexistence equilibria are shown by a saddle-node bifurcation of the level of resource under conditions on competitive effects relatively to associated growth rate per unit of resource.Moreover, we determine the competition outcome in the situations of Balanced and Unbalanced intra-inter species competition effects. Finally, we illustrate results by numerical simulations.


Author(s):  
Janarthanan Ramadoss ◽  
Karthikeyan Rajagopal ◽  
Hayder Natiq ◽  
Iqtadar Hussain

Abstract The master stability function (MSF) is an approach to evaluate the local stability of the synchronization in coupled oscillators. Computing the MSF of a network according to its parameters results in a curve whose shape is dependent on the nodes’ dynamics, network topology, coupling function, and coupling strength. This paper calculates the MSF of networks of two diffusively coupled oscillators by considering different single variable and multi-variable couplings. Then, the linearity of the MSF is investigated by fitting a straight line to the MSF curve, and the root mean square error is obtained. It is observed that the multi-variable coupling with equal coefficients on all variables results in a linear MSF regardless of the dynamics of the nodes.


Nonlinearity ◽  
2021 ◽  
Vol 35 (1) ◽  
pp. 589-607
Author(s):  
Teresa Faria ◽  
Henrique C Prates

Abstract We consider a Nicholson’s equation with multiple pairs of time-varying delays and nonlinear terms given by mixed monotone functions. Sufficient conditions for the permanence, local stability and global attractivity of its positive equilibrium K are established. The main novelty here is the construction of a suitable auxiliary difference equation x n+1 = h(x n ) with h having negative Schwarzian derivative, and its application to derive the attractivity of K for a model with one or more pairs of time-dependent delays. Our criteria depend on the size of some delays, improve results in recent literature and provide answers to open problems.


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