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Forest pests and diseases can diminish forest biodiversity, damage forest ecosystem functions, and have an impact on water conservation. Therefore, it is necessary to analyze the interaction mechanism between plants and pests. In this paper, the prevention and control of a specific pest—namely the larva of Paranthrene tabaniformis (Rott.) (hereinafter referred to as larva)—are studied. Based on the invasion mechanism of the larva in poplar, we establish a delayed differential equation and analyze the existence and stability of equilibria. Next, we assess the existence of a Hopf bifurcation to determine the range of parameters that ensures that the equilibria are stable. Then, we select a set of parameters to verify the results of the stability analysis. Finally, we provide biological explanations and effective theoretical control methods for poplar pests and diseases. [ABSTRACT FROM AUTHOR]

Global warming has brought about enormous damage, therefore, some scholars have begun to conduct in-depth research on peak carbon dioxide emissions and carbon neutrality. In this paper, based on the background of China's upgrading industrial structure and energy structure, we establish a delayed two-dimensional differential equation model associated with China's adjustment of industrial structure. Firstly, we analyze the existence of the equilibrium for the model. We also analyze the characteristic roots of the characteristic equation at each equilibrium point for the model, then, we analyze the stability of the equilibrium point for the model according to the characteristic root, and discuss the existence of Hopf bifurcation of the system by using bifurcation theory. Secondly, we derive the normal form of Hopf bifurcation by using the multiple time scales method. Then, through the official real data, we present the range of some parameters in the model, and determine a set of parameters by reasonable analysis. The validity of the theoretical results is verified by numerical simulations. Finally, we use the real data to forecast the time of peak carbon dioxide emissions and carbon neutralization. Eventually, we put forward some suggestions based on the current situation of carbon emission and absorption in China, such as planting trees to increase the growth rate of carbon absorption, deepening industrial reform and optimizing energy structure to reduce carbon emissions. [ABSTRACT FROM AUTHOR]

A dynamical system for optimal path of energy and resources between two cities in China is considered in this paper. We have discussed dynamics of variables and parameters involved in mentioned system. Bifurcation analysis around non-hyperbolic equilibria is also explained for codimension 1 and 2 bifurcations. Furthermore, double-zero eigenvalue condition is calculated for the proposed model. We have adopted methodology of the generalized vectors for existence of Bogdanov–Takens bifurcation critical point and used analytical computations instead of center manifold theorem for Bogdanov–Takens bifurcation around zero equilibria. Further, with the aid of bifurcation diagram, phase portraits and time history, we discussed occurrence of period doubling, Hopf bifurcation and chaotic region of our proposed model. Based on Lyapunov function and robust control, optimal controllers are designed using Hamilton-Jacobi theorem for the stability of disturbance and aperiodic solution in optimal transportation system (3) due to energy imports from city A to city B. [ABSTRACT FROM AUTHOR]

In this paper, we study a susceptible-infectious-recovered (SIRS) epidemic model with a generalized nonmonotone and saturated incidence rate k I 2 S 1 + β I + α I 2 , in which the infection function first increases to a maximum when a new infectious disease emerges, then decreases due to psychological effect, and eventually tends to a saturation level due to crowding effect. It is shown that there are a weak focus of multiplicity at most two and a cusp of codimension at most two for various parameter values, and the model undergoes saddle-node bifurcation, Bogdanov-Takens bifurcation of codimension two, Hopf bifurcation, and degenerate Hopf bifurcation of codimension two as the parameters vary. It is shown that there exists a critical value α = α 0 for the psychological effect, and two critical values k = k 0 , k 1 (k 0 < k 1) for the infection rate such that: (i) when α > α 0 , or α ≤ α 0 and k ≤ k 0 , the disease will die out for all positive initial populations; (ii) when α = α 0 and k 0 < k ≤ k 1 , the disease will die out for almost all positive initial populations; (iii) when α = α 0 and k > k 1 , the disease will persist in the form of a positive coexistent steady state for some positive initial populations; and (iv) when α < α 0 and k > k 0 , the disease will persist in the form of multiple positive periodic coexistent oscillations and coexistent steady states for some positive initial populations. Numerical simulations, including the existence of one or two limit cycles and data-fitting of the influenza data in Mainland China, are presented to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

Since plant–plant interaction has been the fundamental issue of the ecology community and is essential for the multispecies forest community, it is necessary to analyze the interaction mechanisms and provide suggestions for collaborative management of multispecies forests with the background of double carbon goals in China. To explore the interaction mechanisms in different interaction modes and assist China's green development, we choose the most promising area, the Daxing'an Mountains, and its dominant species, Larch and Betula platyphylla, as research objects and establish a delayed two-species interaction model with an age structure. First, we calculate the equilibria of our model and analyze the stability of equilibria. Then, we study the existence of the Hopf bifurcation near the equilibria. Furthermore, we determine reasonable parameter values based on official data through mathematical methods, such as cluster analysis and model fitting. Finally, we carry out numerical simulations from three aspects, the evolution of a stand structure without interactions, the population dynamics in different interaction modes, and the influences of the parameters on the equilibria. Combined with simulation results, we provide biological interpretations for simulations of the stand structure evolution process and the interactions between Larch and Betula platyphylla; we also give reasonable values of the growth rates and mortalities for developing forest strategies. [ABSTRACT FROM AUTHOR]