Certified Numerical Real Root Isolation for Bivariate Polynomial Systems

2019 ◽  
Author(s):  
Jin-San Cheng ◽  
Junyi Wen
Keyword(s):  
Real Root ◽  
Polynomial Systems ◽  
Bivariate Polynomial ◽  
Root Isolation ◽  
Real Root Isolation

scholarly journals Dynamics of a Prey–Predator System with Foraging Facilitation in Predators

2020 ◽  
Vol 30 (01) ◽  
pp. 2050009
Author(s):  
Yong Yao
Keyword(s):  
Numerical Simulations ◽  
Real Root ◽  
Qualitative Properties ◽  
Isolation Technique ◽  
Root Isolation ◽  
Number Of Equilibria ◽  
Complete Investigation ◽  
Theoretical Results ◽  
Predator System ◽  
Real Root Isolation

The dynamics of a prey–predator system with foraging facilitation among predators are investigated. The analysis involves the computation of many semi-algebraic systems of large degrees. We apply the pseudo-division reduction, real-root isolation technique and complete discrimination system of polynomial to obtain the parameter conditions for the exact number of equilibria and their qualitative properties as well as do a complete investigation of bifurcations including saddle-node, transcritical, pitchfork, Hopf and Bogdanov–Takens bifurcations. Moreover, numerical simulations are presented to support our theoretical results.

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