scholarly journals Modelling and analysis of prey-predator model involving predation of mature prey using delay differential equations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Pankaj Kumar ◽  
Shiv Raj
Keyword(s):  
Sensitivity Analysis ◽  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Critical Point ◽  
Delay Differential Equations ◽  
Equilibrium Points ◽  
State Variables ◽  
Predator Model ◽  
Delay Differential ◽  
Zero Equilibrium

<p style='text-indent:20px;'>In this paper, the modelling and analysis of prey-predator model involving predation of mature prey is done using DDE. Equilibrium points are calculated and stability analysis is performed about non-zero equilibrium point. Delay parameter destabilizes the system and triggers asymptotic stability when value of delay parameter is below the critical point. Hopf bifurcation is observed when the value of delay parameter crosses the critical point. Sensitivity analysis has also been performed to look into the effect of other parameters on the state variables. The numerical results are substantiated using MATLAB.</p>

scholarly journals A Delayed Vaccination Model for Rotavirus Infection

2020 ◽  
Vol 13 (4) ◽  
pp. 840-851
Author(s):  
Florence A. Adongo ◽  
Onyango Omondi Lawrence ◽  
Job Bonyo ◽  
G. O. Lawi ◽  
Ogada A. Elisha
Keyword(s):  
Mathematical Model ◽  
Stability Analysis ◽  
Hopf Bifurcation ◽  
Numerical Analysis ◽  
Delay Differential Equations ◽  
Asymptotically Stable ◽  
Globally Asymptotically Stable ◽  
Rotavirus Infection ◽  
Delay Differential ◽  
Disease Free

In this work, a mathematical model for rotavirus infection incorporating delay differential equations has been formulated. Stability analysis of the model has been performed. The result shows that the Disease Free Equilibrium is globally asymptotically stable and the Endemic Equilibrium undergoes a Hopf bifurcation. Numerical analysis has been performed to validate the analysis.

scholarly journals Pseudospectral Approximation of Hopf Bifurcation for Delay Differential Equations

2021 ◽  
Vol 20 (1) ◽  
pp. 333-370
Author(s):  
B. A. J. de Wolff ◽  
F. Scarabel ◽  
S. M. Verduyn Lunel ◽  
O. Diekmann
Keyword(s):  
Hopf Bifurcation ◽  
Differential Equations ◽  
Delay Differential Equations ◽  
Delay Differential

scholarly journals Stability analysis of stochastic delay differential equations with Markovian switching driven by L${\acute{e}}$vy noise

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yanqiang Chang ◽  
Huabin Chen
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Exponential Stability ◽  
Delay Differential Equations ◽  
Existence And Uniqueness ◽  
Markovian Switching ◽  
Stochastic Delay Differential Equations ◽  
Stochastic Delay ◽  
Almost Surely Exponential Stability ◽  
Delay Differential

<p style='text-indent:20px;'>In this paper, the existence and uniquenesss, stability analysis for stochastic delay differential equations with Markovian switching driven by L<inline-formula><tex-math id="M1">\begin{document}$ \acute{e} $\end{document}</tex-math></inline-formula>vy noise are studied. The existence and uniqueness of such equations is simply shown by using the Picard iterative methodology. By using the generalized integral, the Lyapunov-Krasovskii function and the theory of stochastic analysis, the exponential stability in <inline-formula><tex-math id="M2">\begin{document}$ p $\end{document}</tex-math></inline-formula>th(<inline-formula><tex-math id="M3">\begin{document}$ p\geq2 $\end{document}</tex-math></inline-formula>) for stochastic delay differential equations with Markovian switching driven by L<inline-formula><tex-math id="M4">\begin{document}$ \acute{e} $\end{document}</tex-math></inline-formula>vy noise is firstly investigated. The almost surely exponential stability is also applied. Finally, an example is provided to verify our results derived.</p>

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