# Modeling Complex Living SystemsMathematical Frameworks

Modeling Complex Living Systems: Mathematical Frameworks for Discrete Activity Systems 4.1 Introduction Chapters 2 and 3 were devoted to the analysis of models where the mi- croscopic state, speciﬁcally, the activity was assumed to be a continuous variable deﬁned over bounded or unbounded domains. On the other hand, a variety of physical systems in the life sciences are characterized by ac- tive particles which need a discrete variable to describe their microscopic state. Therefore, it is useful to format the mathematical tools derived in the preceding chapters to this speciﬁc case. Various applications proposed in the chapters which follow show how the modeling of the same system can be developed using either discrete or continuous variables. When both types of mathematical description of the microscopic state can be used, a critical analysis is developed to compare the two technically diﬀerent ways of deriving the mathematical models. Discrete activity models are not introduced to reduce complexity, either concerning modeling or computational aspects or both, but are motivated by speciﬁc modeling requirements. Namely, a discrete variable can be, in some cases, the correct way to describe the microscopic state. The discretization of the microscopic state is generally referred to the activity. However, for some particular systems, it http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

# Modeling Complex Living SystemsMathematical Frameworks

18 pages

/lp/springer-journals/modeling-complex-living-systems-mathematical-frameworks-Tn2KR0DAoZ
Publisher
Birkhäuser Boston
ISBN
978-0-8176-4510-6
Pages
63 –80
DOI
10.1007/978-0-8176-4600-4_4
Publisher site
See Chapter on Publisher Site

### Abstract

for Discrete Activity Systems 4.1 Introduction Chapters 2 and 3 were devoted to the analysis of models where the mi- croscopic state, speciﬁcally, the activity was assumed to be a continuous variable deﬁned over bounded or unbounded domains. On the other hand, a variety of physical systems in the life sciences are characterized by ac- tive particles which need a discrete variable to describe their microscopic state. Therefore, it is useful to format the mathematical tools derived in the preceding chapters to this speciﬁc case. Various applications proposed in the chapters which follow show how the modeling of the same system can be developed using either discrete or continuous variables. When both types of mathematical description of the microscopic state can be used, a critical analysis is developed to compare the two technically diﬀerent ways of deriving the mathematical models. Discrete activity models are not introduced to reduce complexity, either concerning modeling or computational aspects or both, but are motivated by speciﬁc modeling requirements. Namely, a discrete variable can be, in some cases, the correct way to describe the microscopic state. The discretization of the microscopic state is generally referred to the activity. However, for some particular systems, it

Published: Jan 1, 2008

Keywords: Activity Variable; Velocity Variable; Test Particle; Active Particle; Encounter Rate