Chaos in low-dimensional Lotka–Volterra models of competition

Vano, J. A.; Wildenberg, Joseph C.; Anderson, M. B.; Noel, Jimmy; Sprott, Julien Clinton

doi:10.1088/0951-7715/19/10/006

Cited by 124 publications

(101 citation statements)

References 31 publications

(37 reference statements)

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“…However, this impression is wrong, and LV models can represent the most complicated nonlinearities 6 ISRN Biomathematics [21,134], including deterministic chaos. For instance, the graph in Figure 3 is the output of an LV system with just four variables [71,137,138].…”

Section: Types Of Nonlinear Canonical Modelsmentioning

confidence: 99%

Biochemical Systems Theory: A Review

Voit

2013

ISRN Biomathematics

146

154

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Biochemical systems theory (BST) is the foundation for a set of analytical andmodeling tools that facilitate the analysis of dynamic biological systems. is paper depicts major developments in BST up to the current state of the art in 2012. It discusses its rationale, describes the typical strategies and methods of designing, diagnosing, analyzing, and utilizing BST models, and reviews areas of application. e paper is intended as a guide for investigators entering the fascinating �eld of biological systems analysis and as a resource for practitioners and experts. PreambleBiochemical systems theory (BST) is a mathematical and computational framework for analyzing and simulating systems. It was originally developed for biochemical pathways but by now has become much more widely applied to systems throughout biology and beyond. BST is called "canonical, " which means that model construction, diagnosis, and analysis follow stringent rules, which will be discussed throughout this paper. e key ingredient of BST is the power-law representation of all processes in a system.BST has been the focus of a number of books [1-6], including some in Chinese and Japanese [7][8][9]. e most detailed modern text dedicated speci�cally to BST is [3]. Moreover, since its inception, numerous reviews have portrayed the evolving state of the art in BST. Most of these reviews summarized methodological advances for the analysis of biochemical pathway systems . Others compared BST models with alternative modeling frameworks [32,[51][52][53][54][55][56][57][58][59][60][61][62][63]; some of these comparisons will be discussed later. Yet other reviews focused on specialty areas, such as customized methods for optimizing BST models (e.g., [64][65][66][67]) or estimating their parameters (e.g., [68][69][70][71][72]), strategies for discovering design and operating principles in natural system (e.g., [73][74][75][76][77][78]), and even the use of BST models in statistics [79][80][81]. A historical account of the �rst twenty years of BST was presented in [82].Supporting the methodological developments in the �eld, several soware packages were developed for different aspects of BST analysis. e earliest was ESSYNS [83][84][85], which supported all standard steady-state analyses and also contained a numerical solver that, at the time, was many times faster than any off-the-shelf soware [86,87]; see also [88]. Utilizing advances in computing and an extension of the solver from ESSYNS, Ferreira created the very user-friendly package PLAS, which is openly available and still very widely used [89] (see also [3]). Yamada and colleagues developed soware to translate E-cell models into BST models in PLAS format [90]. Okamoto's group created the soware BestKit, which permits the graphical design and translation of models, along with their analysis [91][92][93]. Vera and colleagues developed the soware tool PLMaddon for analyzing BST models within SBML [94]; see also [95]. It expands the Matlab SBToolbox with speci�c functionalities for power-law repr...

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Section: Types Of Nonlinear Canonical Modelsmentioning

confidence: 99%

Biochemical Systems Theory: A Review

Voit

2013

ISRN Biomathematics

146

154

View full text Add to dashboard Cite

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“…For instance, chaos has been observed in models with four competing species (see [142] and the references therein).…”

Section: Initial-value Population Modelsmentioning

confidence: 99%

Diffusive and nondiffusive population models

Jüngel

2010

Modeling and Simulation in Science, Engineering and Technology

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“…The Lotka-Volterra model has been used in various ways to model complex systems [9][10][11][12][13][14][15][16]. For instance, in Ref.…”

Section: Introductionmentioning

confidence: 99%

Effects of competition and cooperation interaction between agents on networks in the presence of a market capacity

et al. 2016

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A network effect is introduced taking into account competition, cooperation, and mixed-type interaction among agents along a generalized Verhulst-Lotka-Volterra model. It is also argued that the presence of a market capacity undoubtedly enforces a definite limit on the agent's size growth. The state stability of triadic agents, i.e., the most basic network plaquette, is investigated analytically for possible scenarios, through a fixed-point analysis. It is discovered that: (i) market demand is only satisfied for full competition when one agent monopolizes the market; (ii) growth of agent size is encouraged in full cooperation; (iii) collaboration among agents to compete against one single agent may result in the disappearance of this single agent out of the market; and (iv) cooperating with two rivals may become a growth strategy for an intelligent agent.

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Chaos in low-dimensional Lotka–Volterra models of competition

Cited by 124 publications

References 31 publications

Biochemical Systems Theory: A Review

Biochemical Systems Theory: A Review

Diffusive and nondiffusive population models

Effects of competition and cooperation interaction between agents on networks in the presence of a market capacity

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