This study focuses on the stability and local bifurcations of a discrete-time SIR epidemic model with logistic growth of the susceptible individuals analytically,and numerically.The analytical results are obtained usi...This study focuses on the stability and local bifurcations of a discrete-time SIR epidemic model with logistic growth of the susceptible individuals analytically,and numerically.The analytical results are obtained using thenormal form technique and numerical results are obtained using the numerical continuation method.For this model,a number of bifurcations are studied,including the transcritical(pitchfork)and fip bifurcations,the Neimark-Sacker(NS)bifurcations,and the strong resonance bifurcations.We especially determine the dynamical behaviors of the model for higher iterations up to fourth-order.Numerical simulation is employed to present a closed invariant curve emerging about an NS point,and its breaking down to several closed invariant curves and eventuality giving rise to a chaotic strange attractor by increasing the bifurcation parameter.展开更多
文摘This study focuses on the stability and local bifurcations of a discrete-time SIR epidemic model with logistic growth of the susceptible individuals analytically,and numerically.The analytical results are obtained using thenormal form technique and numerical results are obtained using the numerical continuation method.For this model,a number of bifurcations are studied,including the transcritical(pitchfork)and fip bifurcations,the Neimark-Sacker(NS)bifurcations,and the strong resonance bifurcations.We especially determine the dynamical behaviors of the model for higher iterations up to fourth-order.Numerical simulation is employed to present a closed invariant curve emerging about an NS point,and its breaking down to several closed invariant curves and eventuality giving rise to a chaotic strange attractor by increasing the bifurcation parameter.
