Self-organized Behaviors Of Fish School With Hydrodynamic Interactions

Collective motions of biological systems have been widely observed in nature,for example the migration of fish and mammals in groups,the spectacular close formation of flying wild geese.Biological groups can spontaneously form specific organized structures,enabling the groups to reduce resistance,save energy,avoid predators,and find food faster.To understand the underlying mechanism of self-organization is not only helpful for human beings to explore nature,but also has a broad bionic engineering prospect.For a fish school living in water,the fluid will inevitably play an important role in the information transmission between individual fish.This research chooses fish school as the research object,to study the responses of a fish school under the threat of predators and also in a boundary-confined zone by proposing a mathematical model,which considers the hydrodynamic interactions between individuals.This research focus on the collective and self-organizing behaviors of the fish school.First,by introducing a predator and considering four different attack tactics,approaching the school at a fixed orientation,moving along a straight trajectory while reversing its direction periodically,chasing the geometric center of the school,and chasing always the nearest prey,the responses of a self-organized milling school to this predator are studied.The fish school exhibits different collective behaviors as they try to avoid the predator.For example,the preys are dispersed,turn around away from the predator,escape in a specific form of polarizing pattern,or they forms smaller groups which can collaborate.Moreover,the average speed of the fish school fluctuates due to the hydrodynamic interactions,which characteristic varies between different attack tactics.Specifically,for the fixed orientation tactic,the fish school will accelerate,while for the chasing center tactic,the school will decelerate.Different delay factors for the predator are also considered,which result in different responses of the fish school.Furthermore,collision avoidance models for the fish group swimming in a bounded domain are proposed,with both circular and square domain considered.The numerical results show that the fish always accumulate locally to a single or a few points at the early stage,but eventually they will reorganize.This research also investigates how the number of individuals changes the collective behavior.