Flip bifurcation and Neimark-Sacker bifurcation in a discrete predator prey model with harvesting

In this paper,a difference-algebraic predator prey model is proposed,and its complex dynamical behaviors are analyzed.The model is a discrete singular system,which is obtained by using Euler scheme to discretize a differential-algebraic predator-prey model with harvesting that we establish.Firstly,the local stability of the interior equilibrium point of proposed model is investigated on the basis of discrete dynamical system the­ory.Further,by applying the new normal form of difference-algebraic equations,center manifold theory and bifurcation theory,the Flip bifurcation and Neimark-Sacker bifur­cation around the interior equilibrium point are studied,where the step size is treated as the variable bifurcation parameter.Lastly,with the help of Matlab software,some numerical simulations are performed not only to validate our theoretical results,but also to show the abundant dynamical behaviors,such as period-doubling bifurcations,period 2,4,8,and 16 orbits,invariant closed curve,and chaotic sets.In particular,the corresponding maximum Lyapunov exponents are numerically calculated to corroborate the bifurcation and chaotic behaviors.

Qualitative Analysis of a Fractional Pandemic Spread Model of the Novel Coronavirus (COVID-19)

In this study,we classify the genera of COVID-19 and provide brief information about the root of the spread and the transmission from animal(natural host)to humans.We establish a model of fractional-order differential equations to discuss the spread of the infection from the natural host to the intermediate one,and from the intermediate one to the human host.At the same time,we focus on the potential spillover of bat-borne coronaviruses.We consider the local stability of the co-existing critical point of the model by using the Routh–Hurwitz Criteria.Moreover,we analyze the existence and uniqueness of the constructed initial value problem.We focus on the control parameters to decrease the outbreak from pandemic form to the epidemic by using both strong and weak Allee Effect at time t.Furthermore,the discretization process shows that the system undergoes Neimark–Sacker Bifurcation under specific conditions.Finally,we conduct a series of numerical simulations to enhance the theoretical findings.