Bifurcations of limit cycles from quintic Hamiltonian systems with a double figure eight loop☆☆The work was supported in part by Australia Research Counsil under the Discovery Projects scheme (grant ID: DP0559111).

AbstractThis paper deals with Liénard equations of the form x˙=y, y˙=P(x)+yQ(x,y), with P and Q polynomials of degree 5 and 4 respectively. Attention goes to perturbations of the Hamiltonian vector fields with an elliptic Hamiltonian of degree six, exhibiting a double figure eight loop. The number of limit cycles and their distributions are given by using the methods of bifurcation theory and qualitative analysis

SVEIRS: A New Epidemic Disease Model with Time Delays and Impulsive Effects

We first propose a new epidemic disease model governed by system of impulsive delay differential equations. Then, based on theories for impulsive delay differential equations, we skillfully solve the difficulty in analyzing the global dynamical behavior of the model with pulse vaccination and impulsive population input effects at two different periodic moments. We prove the existence and global attractivity of the “infection-free” periodic solution and also the permanence of the model. We then carry out numerical simulations to illustrate our theoretical results, showing us that time delay, pulse vaccination, and pulse population input can exert a significant influence on the dynamics of the system which confirms the availability of pulse vaccination strategy for the practical epidemic prevention. Moreover, it is worth pointing out that we obtained an epidemic control strategy for controlling the number of population input

A stage-structured predator-prey si model with disease in the prey and impulsive effects

This paper aims to develop a high-dimensional SI model with stage structure for both the prey (pest) and the predator, and then to investigate the dynamics of it. The model can be used for the study of Integrated Pest Management (IPM) which is a combination of constant pulse releasing of animal enemies and diseased pests at two different fixed moments. Firstly, we use analytical techniques for impulsive delay differential equations to obtain the conditions for global attractivity of the ‘pest-free’ periodic solution and permanence of the population model. It shows that the conditions strongly depend on time delay, impulsive release of animal enemies and infective pests. Secondly, we present a pest management strategy in which the pest population is kept under the economic threshold level (ETL) when the pest population is permanent. Finally, numerical analysis is presented to illustrate our main conclusion

Study on the quality change of crown pear during storage

Using the high-quality Crown Pear as the subject of experimental research, an analysis of the changes in the quality of Crown Pears during a storage period is conducted to provide a theoretical basis for the development of the pear cold storage industry. The study utilizes a handheld digital refractometer, texture analyzer, colorimeter, T-type thermocouple, and electronic balance to explore six aspects of Crown Pears: soluble solids content, hardness, color difference, freezing point, drying loss, and taste. The results reveal the following changes in pear quality during different storage periods within one cycle: the content of soluble solids in Crown Pears initially increases and then decreases during the storage period; hardness decreases with increasing storage time; the external appearance of pears gradually darkens; and drying loss increases with storage time. During the cold storage process of Crown Pears, the optimal temperature setting for the cold storage should be maintained at -1°C to 0.5°C. The flavor of Crown Pears is not optimal during the early stage of storage. The storage time for Crown Pears should be within four months