A Study Of The Spawn-predator System With Transient And Non-transient Pulses

Mathematics is the combination of biology and mathematics,a new discipline biomathematics by development since more than a century,he developed many new branches,such as the law of development and spread of infectious diseases epidemic dynamics,study the interaction between population and environment in ecology and population dynamics of the interactions between the population ecology,etc.But no matter how complex the model is,it is based on a single population model.The single population model is the cornerstone for the development and study of multi-population interactions,complex network models and complex systems in the field of life science.Single population model can accurately depict biological phenomena and the change law of development,because of the model parameters are clear biological significance,theory background and application of rich diversity,single population model basic form the theoretical framework of the system,and the single population model has been widely used in animal and plant growth,biological resource management,integrated pest management and so on traditional and interdisciplinary field.The creatures of nature are in the process of long-term evolution.Due to the constant migration of biological population,internal and external competition of biological population.Rules of biological survival: the law of the jungle,survival of the fittest.It allows the organism to constantly improve itself to adapt to the conditions around it.In order to resist harsh environmental conditions,most organisms reduce their metabolism,lower their body temperature,reduce energy expenditure,and go into a trance state to resist adverse external conditions(lack of food,extreme hot or cold weather,etc.).This is commonly referred to as hibernation or summer hibernation.However,due to human activities,it has caused such problems as unbalanced population competition,habitat destruction and global warming.It has caused great damage to the orderly circulation of the ecosystem.In recent years,due to the overexploitation of the ecological system by human beings,the competition among biological groups,the destruction of the living environment,global warming and other problems have occurred.Therefore,the competitive relationship between biological populations has been studied by many scholars,and the most basic biological birth-predation system is in the competitive relationshipTherefore this paper mainly through the differential equation and other related knowledge to establish the dynamic model.The differential equations of instantaneous pulse birth and non-instantaneous pulse birth are established.Instantaneous and non-instantaneous pulse birth-predation systems were established.(2)The use of ordinary differential equations,the stability of the solution of the system and other relevant advanced mathematical knowledge of the analysis of the system.Find the periodic solution of the system and determine the stability of the system.(3)The biological population analysis,to determine the biological survival or extinction of the relevant data.The problem of preventing the flood of living things or the extinction of large Numbers of people.To protect the stability of the ecosystem.The dynamic model is used to protect organisms and ecosystems through computational research.In this study,ordinary differential equation and other mathematical knowledge are used to establish relevant models through single population model,and the model is analyzed and calculated through the knowledge of system stability solution,so as to find out the equilibrium point of the system and establish the stability of the system.Finally,the survival,extinction and other related issues are discussed and studied...