Bifurcations of a Leslie Gower predator prey model with Holling type III functional response and Michaelis-Menten prey harvesting

Hopf bifurcation of the Michaelis-Menten type ratio-dependent predator-prey model with age structure

This paper is devoted to the study of a predator-prey model with predator-age structure that involves Michaelis-Menten type ratio-dependent functional response. We study some dynamical properties of the model by using the theory of integrated semigroup and the Hopf bifurcation theory for semilinear equations with non-dense domain. The existence of Hopf bifurcation is established by regarding the biological maturation period $τ$ as the bifurcation parameter. The computer simulations and sensitivity analysis on parameters are also performed to illustrate the conclusions.

On the quasi-steady-state approximation in an open Michaelis--Menten reaction mechanism

The conditions for the validity of the standard quasi-steady-state approximation in the Michaelis--Menten mechanism in a closed reaction vessel have been well studied, but much less so the conditions for the validity of this approximation for the system with substrate inflow. We analyze quasi-steady-state scenarios for the open system attributable to singular perturbations, as well as less restrictive conditions. For both settings we obtain distinguished invariant slow manifolds and time scale estimates, and we highlight the special role of singular perturbation parameters in higher order appr…

Properties of the Michaelis-Menten Mechanism in Phase Space

We study the two-dimensional reduction of the Michaelis-Menten reaction of enzyme kinetics. First, we prove the existence and uniqueness of a slow manifold between the horizontal and vertical isoclines. Second, we determine the concavity of all solutions in the first quadrant. Third, we establish the asymptotic behaviour of all solutions near the origin, which generally is not given by a Taylor series. Finally, we determine the asymptotic behaviour of the slow manifold at infinity.

Precluding Oscillations in Michaelis-Menten Approximations of Dual-site Phosphorylation Systems

Oscillations play a major role in a number of biological systems, from predator-prey models of ecology to circadian clocks. In this paper we focus on the question of whether oscillations exist within dual-site phosphorylation systems. Previously, Wang and Sontag showed, using monotone systems theory, that the Michaelis-Menten (MM) approximation of the distributive and sequential dual-site phosphorylation system lacks oscillations. However, biological systems are generally not purely distributive; there is generally some processive behavior as well. Accordingly, this paper focuses on the MM app…

低酶浓度下Michaelis-Menten反应机理准稳态近似的严格估计

Rigorous estimates for the quasi-steady state approximation of the Michaelis-Menten reaction mechanism at low enzyme concentrations

针对Michaelis-Menten反应机理准稳态近似误差缺乏可靠定量估计的问题，结合相平面分析与微分不等式，推导了初始瞬态阶段的严格界值及慢动力学区域的近似精度，给出了Segel-Slemrod参数下的一阶误差估计。

低底物浓度下的Michaelis–Menten反应：准一级动力学与时间尺度分离条件

The Michaelis--Menten reaction at low substrate concentrations: Pseudo-first-order kinetics and conditions for timescale separation

本研究证明低初始底物浓度下Michaelis–Menten反应可由线性系统精确近似得到准一级动力学，给出近似有效性充分条件$s_0 \ll K$，还确定了线性系统时间尺度分离的充要条件并推导约化方程。