Qualitative Analysis of Quadratic Polynomial Dynamical Systems Associated with the Modeling and Monitoring of Oil Fields

2019 ◽  
Vol 40 (10) ◽  
pp. 1695-1710 ◽  
Author(s):  
A. Kh. Shakhverdiev ◽  
Yu. V. Shestopalov
Keyword(s):  
Dynamical Systems ◽  
Qualitative Analysis ◽  
Quadratic Polynomial ◽  
Oil Fields ◽  
Polynomial Dynamical Systems

scholarly journals Qualitative Theory of Two-Dimensional Polynomial Dynamical Systems

Symmetry ◽  
2021 ◽  
Vol 13 (10) ◽  
pp. 1884
Author(s):  
Yury Shestopalov ◽  
Azizaga Shakhverdiev
Keyword(s):  
Dynamical Systems ◽  
Feasible Solution ◽  
Qualitative Theory ◽  
Single Parameter ◽  
Quadratic Polynomial ◽  
Phase Portraits ◽  
Two Dimensional ◽  
Polynomial Dynamical Systems ◽  
Specific Solution ◽  
Integrable Dynamical Systems

A qualitative theory of two-dimensional quadratic-polynomial integrable dynamical systems (DSs) is constructed on the basis of a discriminant criterion elaborated in the paper. This criterion enables one to pick up a single parameter that makes it possible to identify all feasible solution classes as well as the DS critical and singular points and solutions. The integrability of the considered DS family is established. Nine specific solution classes are identified. In each class, clear types of symmetry are determined and visualized and it is discussed how transformations between the solution classes create new types of symmetries. Visualization is performed as series of phase portraits revealing all possible catastrophic scenarios that result from the transition between the solution classes.

Exact Cuspon and Compactons of the Novikov Equation

2014 ◽  
Vol 24 (03) ◽  
pp. 1450037 ◽  
Author(s):  
Jibin Li
Keyword(s):  
Dynamical Systems ◽  
Qualitative Analysis ◽  
Traveling Wave ◽  
Wave Solution ◽  
Traveling Wave Solutions ◽  
Phase Portraits ◽  
Breaking Wave ◽  
Wave Solutions ◽  
Novikov Equation

In this paper, we apply the method of dynamical systems to the traveling wave solutions of the Novikov equation. Through qualitative analysis, we obtain bifurcations of phase portraits of the traveling system and exact cuspon wave solution, as well as a family of breaking wave solutions (compactons). We find that the corresponding traveling system of Novikov equation has no one-peakon solution.

scholarly journals SPECIAL CURVES AND POSTCRITICALLY FINITE POLYNOMIALS

2013 ◽  
Vol 1 ◽  
Author(s):  
MATTHEW BAKER ◽  
LAURA DE MARCO
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Moduli Space ◽  
Dense Subset ◽  
Rational Curves ◽  
Rational Maps ◽  
Complex Polynomial ◽  
Polynomial Dynamical Systems ◽  
Postcritically Finite ◽  
Cubic Polynomials

AbstractWe study the postcritically finite maps within the moduli space of complex polynomial dynamical systems. We characterize rational curves in the moduli space containing an infinite number of postcritically finite maps, in terms of critical orbit relations, in two settings: (1) rational curves that are polynomially parameterized; and (2) cubic polynomials defined by a given fixed point multiplier. We offer a conjecture on the general form of algebraic subvarieties in the moduli space of rational maps on ${ \mathbb{P} }^{1} $ containing a Zariski-dense subset of postcritically finite maps.

Sign in / Sign up

Export Citation Format

Share Document