Threshold policy is more realistic than continuous control for biological system management. Most related works are devoted to studying a single-threshold value for one single population, thereby avoiding complicated mathematical analysis of the nonsmooth differential equations. Based on the fact that numerical simulations play an important role in analyzing and understanding the intrinsic mechanism of a biological experiment and system, we hereby propose a differential linear complementarity system to reformulate the biological system with threshold policy. Using this method, we can transform a biological system with multiple-threshold values for one or more population to a differential linear complementarity system, where the corresponding dynamics can be investigated numerically by various algorithms for the complementarity problem. Firstly, the well-posedness of solutions of the differential linear complementarity system and its discretized method are derived explicitly. Then we illustrate the application of our approach to two systems which are a population harvesting system with threshold policy and an HIV replication system with threshold therapy, respectively. Numerical results demonstrate that those nonsmooth biological systems exhibit much more complex dynamics than the corresponding smooth systems. These results also validate the effectiveness and simplicity of the method that reformulates a common biological system with multiple-threshold policy by a differential linear complementarity system.
AI-powered Research feed
Round-ups are the summaries of handpicked papers around trending topics published every week. These would enable you to scan through a collection of papers and decide if the paper is relevant to you before actually investing time into reading it.
Climate change Research Articles published between Nov 15, 2021 to Nov 21, 2021
Nov 22, 2021
Articles Included: 3
In ‘Climate change adaptation for managing non-timber forest products in the Nepalese Himalaya’, Lila Gurung et al. (2021) noted that non-timber fores...Read More