In this paper, the homotopy analysis method is used for solving a prey-predator system with holling IV functional response. The approximation solutions were obtained by homotopy analysis method, and contain the auxiliary parameter h which provides us with a convenient way to adjust and control convergence region and rate of solution series. This result showed that this method is valid and feasible for the system.

Risk-based inspection analysis is a key part of structure integrity management (SIM) process for ensuring the fitness-for-purpose of offshore jacket platforms. For the platforms locates in the South China Sea which often suffer severe sea condition, it is essential to employ an appropriate assessment method to determine the structure strength and increase the platforms’ safety. This paper presents a comprehensive risk-based inspection method for in-service jacket platform structure. Nonlinear pushover analysis is used to carry out the ultimate bearing capacity and failure consequence of the structure, in which the platform ultimate bearing capacity is characterized in terms of the Reserve Strength Ratio (RSR) and Residual Capacity Ratio (RCR). Taking the four limit state equations of structure member and limit state judgment criteria of structure system into consideration, the structure reliability analysis is proposed with the combination of extreme probability model of environment loads. On this basis, a risk matrix will be formed and a risk-based inspection plan can be developed. A case study of jacket platform located in the South China Sea is used to illustrate the application of the structure assessment approach.

In this letter, we apply the homotopy analysis method (HAM) to obtain analytical solution of the fractional equation where the fractional derivatives are Caputo sense. The example is given to show the efficiency of the method.