Journal ArticleDOI
Classification and dynamics of stably dissipative Lotka–Volterra systems
Xiaohua Zhao,Jigui Luo +1 more
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TLDR
In this paper, a graph-theoretic classification method for stably dissipative matrices is proposed, based on which, for all five-order stable matrices, the associated graphs are classified completely as 27 topologically different graphs and for each graph the dynamics of the corresponding Lotka-Volterra system is discussed.Abstract:
This paper deals with classification and dynamical behaviors of stably dissipative Lotka–Volterra (LV) systems. The sufficient and necessary conditions for a matrix being stably dissipative are discussed firstly. Then, a graph-theoretic classification method for stably dissipative matrices is proposed, based on which, for all five-order stably dissipative matrices, the associated graphs are classified completely as 27 topologically different graphs and for each graph the dynamics of the corresponding LV system is discussed. Finally, the effects of removing some links from the above graphs on the dynamics of the corresponding LV systems are discussed.read more
Citations
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Journal ArticleDOI
Compositional Lotka-Volterra describes microbial dynamics in the simplex.
TL;DR: This work derives a new nonlinear dynamical system for microbial dynamics, termed “compositional” Lotka-Volterra (cLV), unifying approaches from community ecology and compositional data analysis, and investigates when information about direct effects can be recovered from relative data that naively provide information about only indirect effects.
Journal ArticleDOI
The Interconnection of Quadratic Droop Voltage Controllers Is a Lotka-Volterra System: Implications for Stability Analysis
TL;DR: This letter studies the stability of voltage dynamics for a power network in which nodal voltages are controlled by means of quadratic droop controllers with nonlinear AC reactive power as inputs and proves a uniform ultimate boundedness result and investigating conditions under which the network is cooperative.
Journal ArticleDOI
Rank of stably dissipative graphs
Pedro Duarte,Telmo Peixe +1 more
TL;DR: For the class of stably dissipative Lotka-Volterra systems, the rank of the defining matrix, which is the dimension of the associated invariant foliation, is completely determined by the system's graph.
Journal ArticleDOI
Conservative and Dissipative Polymatrix Replicators
TL;DR: In this paper, the authors address a class of replicator dynamics, referred as polymatrix replicators, that contains well known classes of evolutionary game dynamics, such as the symmetric and asymmetric replicator equations, and some replicators equations for $n$-person games.
Dissertation
Lotka-volterra systems and polymatrix replicators
TL;DR: Tese de doutoramento, Matematica (Analise Matematicsa), Universidade de Lisboa, Faculdade de Ciencias, 2015 as discussed by the authors
References
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Book
Applications of Lie Groups to Differential Equations
TL;DR: In this paper, the Cauchy-Kovalevskaya Theorem has been used to define a set of invariant solutions for differential functions in a Lie Group.
Book
Evolutionary games and population dynamics
Josef Hofbauer,Karl Sigmund +1 more
TL;DR: In this book the authors investigate the nonlinear dynamics of the self-regulation of social and economic behavior, and of the closely related interactions among species in ecological communities.
Journal ArticleDOI
Stability theory for ordinary differential equations.
TL;DR: LaSalle stability theorems refined for ordinary differential equations, discussing classical Liapunov results on system stability were discussed in this article, where they were refined for the case of continuous systems.
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