Introduction to algebraic system theory

1983 ◽  
Vol 71 (3) ◽  
pp. 446-446
Author(s):  
R. Saeks
Keyword(s):  
System Theory ◽  
Algebraic System

Towards an Algebraic System Theory Toolbox

1996 ◽  
Vol 29 (1) ◽  
pp. 2697-2702
Author(s):  
Youcef Aït Amirat ◽  
Sette Diop
Keyword(s):  
System Theory ◽  
Algebraic System

scholarly journals A General Principle of Isomorphism: Determining Inverses

Symmetry ◽  
2019 ◽  
Vol 11 (10) ◽  
pp. 1301 ◽  
Author(s):  
Vladimir S. Kulabukhov
Keyword(s):  
System Theory ◽  
General Principle ◽  
Algebraic System ◽  
New Paradigm ◽  
Principle Of Relativity ◽  
The Matrix ◽  
Proven Theorem ◽  
Derived Rules

The problem of determining inverses for maps in commutative diagrams arising in various problems of a new paradigm in algebraic system theory based on a single principle—the general principle of isomorphism is considered. Based on the previously formulated and proven theorem of realization, the rules for determining the inverses for typical cases of specifying commutative diagrams are derived. Simple examples of calculating the matrix maps inverses, which illustrate both the derived rules and the principle of relativity in algebra based on the theorem of realization, are given. The examples also illustrate the emergence of new properties (emergence) in maps in commutative diagrams modeling (realizing) the corresponding systems.

DYNAMIC BEHAVIOR ANALYSIS OF A DIFFERENTIAL-ALGEBRAIC PREDATOR–PREY SYSTEM WITH PREY HARVESTING

2013 ◽  
Vol 21 (03) ◽  
pp. 1350022 ◽  
Author(s):  
WEI LIU ◽  
YUXIAN CHEN ◽  
CHAOJIN FU
Keyword(s):  
System Theory ◽  
Hopf Bifurcation ◽  
Algebraic System ◽  
Bifurcation Theory ◽  
Sufficient Conditions ◽  
Formal Series ◽  
Series Expansions ◽  
Predator Prey ◽  
Prey System ◽  
Differential Algebraic System

This paper studies a differential-algebraic predator–prey system with prey harvesting, which consists of two differential equations and an algebraic equation. By using the differential-algebraic system theory, bifurcation theory and formal series expansions, we investigate the Hopf bifurcation and center stability of the differential-algebraic predator–prey system. Some sufficient conditions on these issues are obtained. In addition, numerical simulations illustrate the effectiveness of our results and their biological implications are discussed.

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