The coronavirus disease(COVID-19)is a dangerous pandemic and it spreads to many people in most of the world.In this paper,we propose a COVID-19 model with the assumption that it is affected by randomness.For positivit...The coronavirus disease(COVID-19)is a dangerous pandemic and it spreads to many people in most of the world.In this paper,we propose a COVID-19 model with the assumption that it is affected by randomness.For positivity,we prove the global existence of positive solution and the system exhibits extinction under certain parametric restrictions.Moreover,we establish the stability region for the stochastic model under the behavior of stationary distribution.The stationary distribution gives the guarantee of the appearance of infection in the population,Besides that,we find the reproduction ratio R for prevail and disappear of infection within the human population.From the graphical representation,we have validated the threshold conditions that define in our theoretical findings.展开更多
Our aim is to study the Hopf bifurcation and synchronisation of a fractional-order butterfly-fishchaotic system. First, we derived the existence of a chaotic attractor in the fractional-order systemand also synchronis...Our aim is to study the Hopf bifurcation and synchronisation of a fractional-order butterfly-fishchaotic system. First, we derived the existence of a chaotic attractor in the fractional-order systemand also synchronisation problem between two identical fractional-order chaotic systems isstudied. Also, control design for the synchronisation with a suitable linear controller is tested inthe response system. Finally, numerical simulation results are provided to confirm the theoreticalanalysis.展开更多
This paper deals with stochastic Chikungunya(CHIKV)virus model along with saturated incidence rate.We show that there exists a unique global positive solution and also we obtain the conditions for the disease to be ex...This paper deals with stochastic Chikungunya(CHIKV)virus model along with saturated incidence rate.We show that there exists a unique global positive solution and also we obtain the conditions for the disease to be extinct.We also discuss about the existence of a unique ergodic stationary distribution of the model,through a suitable Lyapunov function.The stationary distribution validates the occurrence of disease;through that,we find the threshold value for prevail and disappear of disease within host.With the help of numerical simulations,we validate the stochastic reproduction number Rq as stated in our theoretical findings.展开更多
In this paper,we modeled a prey–predator system with interference among predators using the Crowley–Martin functional response.The local stability and existence of Hopf bifurcation at the coexistence equilibrium of ...In this paper,we modeled a prey–predator system with interference among predators using the Crowley–Martin functional response.The local stability and existence of Hopf bifurcation at the coexistence equilibrium of the system in the absence of diffusion are analyzed.Further,the stability of bifurcating periodic solutions is investigated.We derived the conditions for which nontrivial equilibrium is globally asymptotically stable.In addition,we study the diffusion driven instability,Hopf bifurcation of the corresponding diffusion system with zero flux boundary conditions and the Turing instability region regarding parameters are established.The stability and direction of Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem.Numerical simulations are performed to illustrate the theoretical results.展开更多
基金the DST-INSPIRE Fellowship(No.DST/INSPIRE Fellowship/2017/IF170244)Department of Science and Technology,New Delhi.The second author is thankful to the DST-FIST(Grant No.SR/FST/MSI-115/2016(Level-I))DST,New Delhi for providing financial support.The last author was supported by the National Research Foundation of Korea(NRF)grant funded by the Korea government(MSIT)(No.2021R1F1A1048937).
文摘The coronavirus disease(COVID-19)is a dangerous pandemic and it spreads to many people in most of the world.In this paper,we propose a COVID-19 model with the assumption that it is affected by randomness.For positivity,we prove the global existence of positive solution and the system exhibits extinction under certain parametric restrictions.Moreover,we establish the stability region for the stochastic model under the behavior of stationary distribution.The stationary distribution gives the guarantee of the appearance of infection in the population,Besides that,we find the reproduction ratio R for prevail and disappear of infection within the human population.From the graphical representation,we have validated the threshold conditions that define in our theoretical findings.
文摘Our aim is to study the Hopf bifurcation and synchronisation of a fractional-order butterfly-fishchaotic system. First, we derived the existence of a chaotic attractor in the fractional-order systemand also synchronisation problem between two identical fractional-order chaotic systems isstudied. Also, control design for the synchronisation with a suitable linear controller is tested inthe response system. Finally, numerical simulation results are provided to confirm the theoreticalanalysis.
基金supported by the DST-INSPIRE Fellowship(No.DST/INSPIRE Fellowship/2017/IF 170244)Department of Science and Technology,New Delhi.The second author is thankful to UGC(BSR)Start-Up Grant(Grant No.F.30-361/2017(BSR))University Grants Commission,New Delhi.
文摘This paper deals with stochastic Chikungunya(CHIKV)virus model along with saturated incidence rate.We show that there exists a unique global positive solution and also we obtain the conditions for the disease to be extinct.We also discuss about the existence of a unique ergodic stationary distribution of the model,through a suitable Lyapunov function.The stationary distribution validates the occurrence of disease;through that,we find the threshold value for prevail and disappear of disease within host.With the help of numerical simulations,we validate the stochastic reproduction number Rq as stated in our theoretical findings.
基金The second author is thankful to UGC(BSR)-Start Up Grant(Grant No.F.30-361/2017(BSR))University Grants Commission,New Delhi and the DST-FIST(Grant No.SR/FST/MSI-115/2016(Level-I))DST,New Delhi for providing financial support.
文摘In this paper,we modeled a prey–predator system with interference among predators using the Crowley–Martin functional response.The local stability and existence of Hopf bifurcation at the coexistence equilibrium of the system in the absence of diffusion are analyzed.Further,the stability of bifurcating periodic solutions is investigated.We derived the conditions for which nontrivial equilibrium is globally asymptotically stable.In addition,we study the diffusion driven instability,Hopf bifurcation of the corresponding diffusion system with zero flux boundary conditions and the Turing instability region regarding parameters are established.The stability and direction of Hopf bifurcation are determined by applying the normal form theory and the center manifold theorem.Numerical simulations are performed to illustrate the theoretical results.
