biblio.bib

@article{Hof-evol,
    author = {Josef Hofbauer and Karl Sigmund},
    issn = {0033-5770},
    journal = {The Quarterly review of biology},
    language = {eng},
    number = {4},
    %pages = {493-493},
    title = {The Theory of Evolution and Dynamical Systems: Mathematical Aspects of Selection},
    volume = {64},
    year = {1989},
}

@article{Gav,
	doi = {10.1088/1742-6596/55/1/008},
	url = {https://doi.org/10.1088/1742-6596/55/1/008},
	year = 2006,
	month = dec,
	publisher = {{IOP} Publishing},
	volume = {55},
	pages = {80--93},
	author = {C. Gavin and A. Pokrovskii and M. Prentice and V. Sobolev},
	title = {Dynamics of a Lotka-Volterra type model with applications to marine phage population dynamics},
	journal = {Journal of Physics: Conference Series},
	abstract = {The famous Lotka-Volterra equations play a fundamental role in the mathematical modeling of various ecological and chemical systems. A new modification of these equations has been recently suggested to model the structure of marine phage populations, which are the most abundant biological entities in the biosphere. The purpose of the paper is: (i) to make some methodical remarks concerning this modification; (ii) to discuss new types of canards which arise naturally in this context; (iii) to present results of some numerical experiments.}
}

@book{Tak,
    author = {Takeuchi, Y.},
    address = {Singapore ;},
    abstract = {Mathematical ecology is a subject which recently attracts attentions of many mathematicians and biologists. One of the most important and fundamental mathematical models in ecology is of Lotka-Volterra type. This book gives global dynamical properties of L-V systems. The properties analyzed are global stability of the equilibria, persistence or permanence of the systems (which ensures the survival of all the biological-species composed of the systems for the long term) and the existence of periodic or chaotic solutions. The special subject of this book is to consider the effects of the systems},
    isbn = {981-283-054-5},
    keywords = {Population biology -- Mathematical models},
    language = {eng},
    lccn = {96200751},
    publisher = {World Scientific},
    title = {Global dynamical properties of Lotka-Volterra systems},
    year = {1996},
}

@book{Hof-games,
    author = {Hofbauer, Josef},
    address = {Cambridge [etc},
    isbn = {0521623650},
    keywords = {Spieltheorie},
    language = {eng},
    publisher = {Cambridge University Press},
    title = {Evolutionary games and population dynamics},
    year = {1998},
}


@book{Adr,
	author = {Adrianova, L. Ya.},
	isbn = {1-4704-4563-8},
	language = {eng},
	publisher = {American Mathematical Society},
	title = {Introduction to Linear Systems of Differential Equations}
}

@book{Rob,
    abstract = {This book gives a mathematical treatment of the introduction to qualitative differential equations and discrete dynamical systems. The treatment includes theoretical proofs, methods of calculation, and applications. The two parts of the book, continuous time of differential equations and discrete time of dynamical systems, can be covered independently in one semester each or combined together into a year long course. The material on differential equations introduces the qualitative or geometric approach through a treatment of linear systems in any dimension. There follows chapters where equilibria are the most important feature, where scalar (energy) functions is the principal tool, where periodic orbits appear, and finally, chaotic systems of differential equations. The many different approaches are systematically introduced through examples and theorems. The material on discrete dynamical systems starts with maps of one variable and proceeds to systems in higher dimensions. The treatment starts with examples where the periodic points can be found explicitly and then introduces symbolic dynamics to analyze where they can be shown to exist but not given in explicit form. Chaotic systems are presented both mathematically and more computationally using Lyapunov exponents. With the one-dimensional maps as models, the multidimensional maps cover the same material in higher dimensions. This higher dimensional material is less computational and more conceptual and theoretical. The final chapter on fractals introduces various dimensions which is another computational tool for measuring the complexity of a system. It also treats iterated function systems which give examples of complicated sets. In the second edition of the book, much of the material has been rewritten to clarify the presentation. Also, some new material has been included in both parts of the book. This book can be used as a textbook for an advanced undergraduate course on ordinary differential equations and/or dynamical systems. Prerequisites are standard courses in calculus (single variable and multivariable), linear algebra, and introductory differential equations.},
    author = {Robinson, R. Clark},
    address = {Providence},
    booktitle = {An Introduction to Dynamical Systems},
    isbn = {0821891359},
    keywords = {Mechanics of particles and systems ; Nonlinear dynamics},
    language = {eng},
    publisher = {American Mathematical Society},
    title = {An Introduction to Dynamical Systems: Continuous and Discrete, Second Edition},
    year = {2012},
}
    
@book{Hir,
    author = { Morris W. Hirsch and Stephen Smalle},
    address = {New York},
    isbn = {0123495504},
    keywords = {Équations différentielles},
    language = {eng},
    lccn = {73018951},
    publisher = {Academic Press},
    series = {Pure and applied mathematics 60},
    title = {Differential equations, dynamical systems, and linear algebra},
    year = {1974},
}

@book{Codd,
    author = { Earl A. Coddington and Norman Levinson},
    address = {Malabar, Fla},
    edition = {[Reprint Ed.]},
    isbn = {0898747554},
    keywords = {GEWÖHNLICHE DIFFERENTIALGLEICHUNGEN (ANALYSIS)},
    language = {eng},
    publisher = {Krieger},
    title = {Theory of ordinary differential equations},
    year = {1984},
}

@book{alma990043472520205516,
publisher = {World Scientific},
series = {Advanced series in nonlinear dynamics vol. 17},
address = {Singapore},
isbn = {9810245998},
title = {Smooth dynamical systems},
author = { M. C. Irwin},
keywords = {DYNAMISCHE SYSTEME (ANALYSIS)},
language = {eng},
year = {2001},
}


@book{Rob_plus,
	address = {Boca Raton [etc},
	author = {Robinson, R. Clark},
	booktitle = {Dynamical systems stability, symbolic dynamics, and chaos},
	edition = {Second ed.},
	isbn = {9780849384950},
	keywords = {BIFURKATIONEN (PARTIELLE DIFFERENTIALGLEICHUNGEN)},
	language = {eng},
	publisher = {CRC Press},
	series = {Studies in advanced mathematics},
	title = {Dynamical systems : stability, symbolic dynamics, and chaos},
	year = {1999}
}

% @misc{ wiki:xxx,
%   author = "Wikimedia Commons",
%   title = "File:LinearFields.png --- Wikimedia Commons{,} the free media repository",
%   year = "2021",
%   url = "https://commons.wikimedia.org/w/index.php?title=File:LinearFields.png&oldid=525460678",
%   note = "[Online; accessed 13-June-2021]"
% }