Dynamic light regimes strongly impact microalgal photosynthesis efficiency. Finding the optimal way to supply light is then a tricky problem, especially when the growth rate is inhibited by overexposition to light and, at the same time, there is a lack of light in the deepest part of the culture. In this paper, we use the Han model to study the the...
Published in Nonlinearity
In their seminal paper (2008 Chaos 18 037113), Ott and Antonsen showed that large groups of phase oscillators driven by a certain type of common force display low dimensional long-term dynamics, which is described by a small number of ordinary differential equations. This fact was later used as a simplifying reduction technique in many studies of s...
Published in Journal of biological dynamics
In this paper, a general predator-prey model with state-dependent impulse is considered. Based on the geometric analysis and Poincaré map or successor function, we construct three typical types of Bendixson domains to obtain some sufficient conditions for the existence of order-1 periodic solutions. At the same time, the existing domains are discus...
Published in Journal of biological dynamics
In this paper, we study the periodic and stable dynamics of an interactive wild and sterile mosquito population model with density-dependent survival probability. We find a release amount upper bound G∗, depending on the release waiting period T, such that the model has exactly two periodic solutions, with one stable and another unstable, provided ...
Published in Nonautonomous Dynamical Systems
A non-autonomous discrete commensal symbiosis model with Hassell-Varley type functional response is proposed and studied in this paper. Sufficient conditions are obtained for the existence of positive periodic solution of the system.
Published in Open Mathematics
In this paper, a discrete Leslie-Gower predator-prey system with Michaelis-Menten type harvesting is studied. Conditions on the existence and stability of fixed points are obtained. It is shown that the system can undergo fold bifurcation, flip bifurcation, and Neimark-Sacker bifurcation by using the center manifold theorem and bifurcation theory. ...
Published in Nonlinearity
In this paper a generalised Rayleigh–Liénard oscillator is consider and lower bounds for the number of limit cycles bifurcating from weak focus equilibria and saddle connections are provided. By assuming some open conditions on the parameters of the considered system the existence of up to twelve limit cycles is provided. More precisely, the approa...
Published in Partial Differential Equations and Applications
We first take into account variational problems with periodic boundary conditions, and briefly recall some sufficient conditions for a periodic solution of the Euler–Lagrange equation to be either a directional, a weak, or a strong local minimizer. We then apply the theory to circular orbits of the Kepler problem with potentials of type 1/rα,α>0\do...
Published in Acta Mathematica Sinica, English Series
In this paper, we consider the brake orbits of a reversible even Hamiltonian system near an equilibrium. Let the Hamiltonian system (HS) ẋ = JH′(x) satisfies H(0) = 0, H′(0) = 0, reversible and even conditions H(Nx) = H(x) and H(−x) = H(x) for all x ∈ ℝ2n. Suppose the quadratic form Q(x)=12〈H′′(0)x,x〉\documentclass[12pt]{minimal} \usepackage{amsmat...
Published in Journal of Mathematical Biology
The use of predator–prey models in theoretical ecology has a long history, and the model equations have largely evolved since the original Lotka–Volterra system towards more realistic descriptions of the processes of predation, reproduction and mortality. One important aspect is the recognition of the fact that the growth of a population can be sub...
