On a class of polynomial systems of equations following from the formula for total probability and possibilities for eliminating search in solving them

1996 ◽  
pp. 161-173
Author(s):  
An. A. Muchnik
Keyword(s):  
Polynomial Systems ◽  
Total Probability ◽  
Systems Of Equations

scholarly journals Accelerated Solution of Multivariate Polynomial Systems of Equations

2003 ◽  
Vol 32 (2) ◽  
pp. 435-454 ◽  
Author(s):  
B. Mourrain ◽  
V. Y. Pan ◽  
O. Ruatta
Keyword(s):  
Polynomial Systems ◽  
Systems Of Equations ◽  
Multivariate Polynomial

Solving Polynomial Systems for the Kinematic Analysis and Synthesis of Mechanisms and Robot Manipulators

1995 ◽  
Vol 117 (B) ◽  
pp. 71-79 ◽  
Author(s):  
M. Raghavan ◽  
B. Roth
Keyword(s):  
Kinematic Analysis ◽  
State Of The Art ◽  
Polynomial Systems ◽  
The State ◽  
Polynomial Equations ◽  
Systems Of Equations ◽  
Synthesis Of Mechanisms ◽  
Analysis And Synthesis ◽  
Systems Of Polynomial Equations ◽  
And Robotics

Problems in mechanisms analysis and synthesis and robotics lead naturally to systems of polynomial equations. This paper reviews the state of the art in the solution of such systems of equations. Three well-known methods for solving systems of polynomial equations, viz., Dialytic Elimination, Polynomial Continuation, and Grobner bases are reviewed. The methods are illustrated by means of simple examples. We also review important kinematic analysis and synthesis problems and their solutions using these mathematical procedures.

Multiple bifurcation in a predator–prey system with nonmonotonic predator response

1992 ◽  
Vol 120 (3-4) ◽  
pp. 313-347 ◽  
Author(s):  
Franz Rothe ◽  
Douglas S. Shafer
Keyword(s):  
Stable Equilibrium ◽  
Polynomial Systems ◽  
Systems Of Equations ◽  
Predator Prey ◽  
Codimension Two ◽  
Prey System ◽  
Bifurcation Phenomena ◽  
Quartic Polynomial ◽  
Smooth Perturbation ◽  
Predator Response

SynopsisA model of a predator–prey system showing group defence on the part of the prey is formulated, and reduced to a three-parameter family of quartic polynomial systems of equations. Mathematically, this system contains the Volterra–Lotka system, and yields numerous kinds of bifurcation phenomena, including a codimension-two singularity of cusp type, in a neighbourhood of which the quartic system realises every phase portrait possible under small smooth perturbation. Biologically, the nonmonotonic behaviour of the predator response function allows existence of a second singularity in the first quadrant, so that the system exhibits an enrichment paradox, and, for certain choices of parameters, coexistence of stable oscillation and a stable equilibrium.

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