The effect of the alternative resource and time delay on conservation of forestry biomass is studied by considering a nonlinear mathematical model. In this paper, interaction between forestry biomass, industrializatio...The effect of the alternative resource and time delay on conservation of forestry biomass is studied by considering a nonlinear mathematical model. In this paper, interaction between forestry biomass, industrialization pressure, toxicant pressure and technological effort is proposed and analysed. We find out the critical value of delay and observe that there is Hopf bifurcation. Using the normal form theory and the center manifold theorem, we determine the stability and direction of the bifurcating periodic solutions. Numerical simulations are given to illustrate the analytical results.展开更多
Nowadays, management and regulation of natural resources like agriculture, fisheries, forestry and wildlife is one of the popular topics in research. The evolution of humankind is largely dependent on the quality of t...Nowadays, management and regulation of natural resources like agriculture, fisheries, forestry and wildlife is one of the popular topics in research. The evolution of humankind is largely dependent on the quality of the environment and the resources it provides;but numerous human-induced factors, and climate change may drastically alter the conditions of human sustainability. This paper deals with effect of numerous human-induced activities on the depletion of forestry resources and wildlife population with habitat complexity. A nonlinear mathematical model is proposed and analyzed. In modeling process, we assume that the growth rate of wildlife population wholly depends on forestry biomass. It is depleted by human-induced activities. Local stability analysis of the mathematical model along with the persistence of the system is checked by using theory of nonlinear ordinary differential equations and Butler-McGhee lemma. Analytical results obtained are justified numerically through numerical simulation. Important parameters are investigated and variation of variables with change in these parameters is determined.展开更多
This research paper aims at studying the impact of lockdown on the dynamics of novel Corona Virus Disease(COVID-19)emerged in Wuhan city of China in December 2019.Perceiving the pandemic situation throughout the world...This research paper aims at studying the impact of lockdown on the dynamics of novel Corona Virus Disease(COVID-19)emerged in Wuhan city of China in December 2019.Perceiving the pandemic situation throughout the world,Government of India restricted international passenger traffic through land check post(Liang,2020)and imposed complete lockdown in the country on 24 March 2020.To study the impact of lockdown on disease dynamics we consider a three-dimensional mathematical model using nonlinear ordinary differential equations.The proposed model has been studied using stability theory of nonlinear ordinary differential equations.Basic reproduction ratio is computed and significant parameters responsible to keep basic reproduction ratio less than one are identified.The study reveals that disease vanishes from the system only if complete lockdown is imposed otherwise disease will always persist in the population.However,disease can be kept under control by implementing contact tracing and quarantine measures as well along with lockdown if lockdown is imposed partially.展开更多
文摘The effect of the alternative resource and time delay on conservation of forestry biomass is studied by considering a nonlinear mathematical model. In this paper, interaction between forestry biomass, industrialization pressure, toxicant pressure and technological effort is proposed and analysed. We find out the critical value of delay and observe that there is Hopf bifurcation. Using the normal form theory and the center manifold theorem, we determine the stability and direction of the bifurcating periodic solutions. Numerical simulations are given to illustrate the analytical results.
文摘Nowadays, management and regulation of natural resources like agriculture, fisheries, forestry and wildlife is one of the popular topics in research. The evolution of humankind is largely dependent on the quality of the environment and the resources it provides;but numerous human-induced factors, and climate change may drastically alter the conditions of human sustainability. This paper deals with effect of numerous human-induced activities on the depletion of forestry resources and wildlife population with habitat complexity. A nonlinear mathematical model is proposed and analyzed. In modeling process, we assume that the growth rate of wildlife population wholly depends on forestry biomass. It is depleted by human-induced activities. Local stability analysis of the mathematical model along with the persistence of the system is checked by using theory of nonlinear ordinary differential equations and Butler-McGhee lemma. Analytical results obtained are justified numerically through numerical simulation. Important parameters are investigated and variation of variables with change in these parameters is determined.
基金This work is partially supported by UGC-BSR Startup grant Number 30e466/2019(BSR)for which the authors thankfully acknowledge.
文摘This research paper aims at studying the impact of lockdown on the dynamics of novel Corona Virus Disease(COVID-19)emerged in Wuhan city of China in December 2019.Perceiving the pandemic situation throughout the world,Government of India restricted international passenger traffic through land check post(Liang,2020)and imposed complete lockdown in the country on 24 March 2020.To study the impact of lockdown on disease dynamics we consider a three-dimensional mathematical model using nonlinear ordinary differential equations.The proposed model has been studied using stability theory of nonlinear ordinary differential equations.Basic reproduction ratio is computed and significant parameters responsible to keep basic reproduction ratio less than one are identified.The study reveals that disease vanishes from the system only if complete lockdown is imposed otherwise disease will always persist in the population.However,disease can be kept under control by implementing contact tracing and quarantine measures as well along with lockdown if lockdown is imposed partially.
