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This book illustrates how models of complex systems are built up and provides indispensable mathematical tools for studying their dynamics. This second edition includes more recent research results and many new and improved worked out examples and exercises.
The essential points of this ?rst chapter are - The de?nition of a complex system - The notion of emergence - The de?nition of a model - The notion of dynamical system This book is about the dynamics of complex systems. Roughly speaking, a system is a collection of interacting elements making up a whole such as, for instance, a mechanical clock. While many systems may be quite complicated, they are not necessarily considered to be complex. Today, most authors agree on the essential properties a system has to possess to be called complex. The ?rst section is devoted to the description of these properties. To interpret the time evolution of a system, scientists build up models, which are simpli?ed mathematical representations of the system. The exact purpose of a model and what its essential features should be is explained in the second section. The mathematical models that will be discussed in this book are dynami- 1 calsystems. A dynamical system is essentially a set of equationswhose- lutiondescribesthe evolution,asafunction oftime, ofthe state ofthe system. There exist di?erent types of dynamical systems. Some of them are de?ned in the third section. 1 There is an extensive literature on mathematical modeling. The reader may, for example, consult [11,88,163,233].
The essential points of this ?rst chapter are - The de?nition of a complex system - The notion of emergence - The de?nition of a model - The notion of dynamical system This book is about the dynamics of complex systems. Roughly speaking, a system is a collection of interacting elements making up a whole such as, for instance, a mechanical clock. While many systems may be quite complicated, they are not necessarily considered to be complex. Today, most authors agree on the essential properties a system has to possess to be called complex. The ?rst section is devoted to the description of these properties. To interpret the time evolution of a system, scientists build up models, which are simpli?ed mathematical representations of the system. The exact purpose of a model and what its essential features should be is explained in the second section. The mathematical models that will be discussed in this book are dynami- 1 calsystems. A dynamical system is essentially a set of equationswhose- lutiondescribesthe evolution,asafunction oftime, ofthe state ofthe system. There exist di?erent types of dynamical systems. Some of them are de?ned in the third section. 1 There is an extensive literature on mathematical modeling. The reader may, for example, consult [11,88,163,233].
From the reviews of the second edition:
"Boccara's approach is firmly based on dynamical systems theory, differential equations, and maps, with a very solid mathematical treatment, cast at times in terms of definitions and theorems. ... The book is very well suited for graduate or advanced undergraduate studies and comes with a problem and solution section at the end of every chapter. ... The book covers in any case a plethora of models and is highly recommendable for everybody wishing to attain a good knowledge of classical complex system theory." (Claudius Gros, SIAM Review, Vol. 53 (4), 2011)
"Boccara's approach is firmly based on dynamical systems theory, differential equations, and maps, with a very solid mathematical treatment, cast at times in terms of definitions and theorems. ... The book is very well suited for graduate or advanced undergraduate studies and comes with a problem and solution section at the end of every chapter. ... The book covers in any case a plethora of models and is highly recommendable for everybody wishing to attain a good knowledge of classical complex system theory." (Claudius Gros, SIAM Review, Vol. 53 (4), 2011)