ON THE MATHEMATICAL THEORY OF THE DYNAMICS OF SWARMS VIEWED AS COMPLEX SYSTEMS

2012 ◽  
Vol 22 (supp01) ◽  
pp. 1140006 ◽  
Author(s):  
N. BELLOMO ◽  
J. SOLER
Keyword(s):  
Complex System ◽  
Kinetic Theory ◽  
Statistical Mechanics ◽  
Complex Systems ◽  
Modeling And Simulation ◽  
Mathematical Theory ◽  
Stochastic Games ◽  
Microscopic Scale

This paper deals with the modeling and simulation of swarms viewed as a living, hence complex, system. The approach is based on methods of kinetic theory and statistical mechanics, where interactions at the microscopic scale are nonlinearly additive and modeled by stochastic games.

ON A MATHEMATICAL THEORY OF COMPLEX SYSTEMS ON NETWORKS WITH APPLICATION TO OPINION FORMATION

2013 ◽  
Vol 24 (02) ◽  
pp. 405-426 ◽  
Author(s):  
D. KNOPOFF
Keyword(s):  
Kinetic Theory ◽  
Complex Systems ◽  
Mathematical Theory ◽  
Stochastic Games ◽  
Mathematical Structure ◽  
Opinion Formation ◽  
Active Particles ◽  
Mathematical Equations

This paper presents a development of the so-called kinetic theory for active particles to the modeling of living, hence complex, systems localized in networks. The overall system is viewed as a network of interacting nodes, mathematical equations are required to describe the dynamics in each node and in the whole network. These interactions, which are nonlinearly additive, are modeled by evolutive stochastic games. The first conceptual part derives a general mathematical structure, to be regarded as a candidate towards the derivation of models, suitable to capture the main features of the said systems. An application on opinion formation follows to show how the theory can generate specific models.

ON THE DIFFICULT INTERPLAY BETWEEN LIFE, "COMPLEXITY", AND MATHEMATICAL SCIENCES

2013 ◽  
Vol 23 (10) ◽  
pp. 1861-1913 ◽  
Author(s):  
N. BELLOMO ◽  
D. KNOPOFF ◽  
J. SOLER
Keyword(s):  
Kinetic Theory ◽  
Complex Systems ◽  
Case Studies ◽  
Mathematical Theory ◽  
Stochastic Games ◽  
Mathematical Structure ◽  
Living Systems ◽  
Active Particles ◽  
Suitable Generalization ◽  
Mathematical Sciences

This paper presents a revisiting, with developments, of the so-called kinetic theory for active particles, with the main focus on the modeling of nonlinearly additive interactions. The approach is based on a suitable generalization of methods of kinetic theory, where interactions are depicted by stochastic games. The basic idea consists in looking for a general mathematical structure suitable to capture the main features of living, hence complex, systems. Hopefully, this structure is a candidate towards the challenging objective of designing a mathematical theory of living systems. These topics are treated in the first part of the paper, while the second one applies it to specific case studies, namely to the modeling of crowd dynamics and of the immune competition.

LOOKING FOR NEW PARADIGMS TOWARDS A BIOLOGICAL-MATHEMATICAL THEORY OF COMPLEX MULTICELLULAR SYSTEMS

2006 ◽  
Vol 16 (07) ◽  
pp. 1001-1029 ◽  
Author(s):  
NICOLA BELLOMO ◽  
GUIDO FORNI
Keyword(s):  
Kinetic Theory ◽  
Complex Systems ◽  
Critical Analysis ◽  
Mathematical Theory ◽  
Classical Mechanics ◽  
Biological Functions ◽  
Living Matter ◽  
Research Perspectives ◽  
Active Particles ◽  
Large Systems

This paper deals with the development of new paradigms based on the methods of the mathematical kinetic theory for active particles to model the dynamics of large systems of interacting cells. Interactions are ruled, not only by laws of classical mechanics, but also by a few biological functions which are able to modify the above laws. The paper technically shows, also by reasoning on specific examples, how the theory can be applied to model large complex systems in biology. The last part of the paper deals with a critical analysis and with the indication of research perspectives concerning the challenging target of developing a biological-mathematical theory for the living matter.

FROM THE MATHEMATICAL KINETIC THEORY TO MODELLING COMPLEX SYSTEMS IN APPLIED SCIENCES

2004 ◽  
Vol 18 (04n05) ◽  
pp. 487-500 ◽  
Author(s):  
NICOLA BELLOMO
Keyword(s):  
Applied Sciences ◽  
Kinetic Theory ◽  
Statistical Mechanics ◽  
Complex Systems ◽  
Nonequilibrium Statistical Mechanics ◽  
Classical Mechanics ◽  
Large Complex ◽  
Large Systems

This paper deals with the design of a nonequilibrium statistical mechanics theory developed to model large systems of interacting individuals. Interactions being ruled, not only by laws of classical mechanics, but also by some intelligent or organized behaviour. The paper technically shows, also by reasoning on specific examples, how the theory can be applied to model large complex systems in natural and applied sciences.

Statistical Mechanics, Kinetic Theory, and Stochastic Processes

Physics Today ◽  
1973 ◽  
Vol 26 (12) ◽  
pp. 57-59 ◽  
Author(s):  
C. V. Heer ◽  
E. A. Mason
Keyword(s):  
Kinetic Theory ◽  
Statistical Mechanics ◽  
Stochastic Processes

In-Between and Through: Architecture and Complexity

2005 ◽  
Vol 3 (3) ◽  
pp. 335-354 ◽  
Author(s):  
Clarissa Ribeiro Pereira de Almeida ◽  
Anja Pratschke ◽  
Renata La Rocca
Keyword(s):  
Complex System ◽  
Software Engineering ◽  
Complex Systems ◽  
Design Process ◽  
Three Dimensional ◽  
Self Organization ◽  
Three Dimensional Modeling ◽  
Dimensional Modeling ◽  
Complex Thought ◽  
Basic Characteristics

This paper draws on current research on complexity and design process in architecture and offers a proposal for how architects might bring complex thought to bear on the understanding of design process as a complex system, to understand architecture as a way of organizing events, and of organizing interaction. Our intention is to explore the hypothesis that the basic characteristics of complex systems – emergence, nonlinearity, self-organization, hologramaticity, and so forth – can function as effective tools for conceptualization that can usefully extend the understanding of the way architects think and act throughout the design process. To illustrate the discussions, we show how architects might bring complex thought inside a transdisciplinary design process by using models such as software engineering diagrams, and three-dimensional modeling network environments such as media to integrate, connect and ‘trans–act’.

scholarly journals Toward Reverse Engineering to Economic Analysis: An Overview of Tools and Methodology

2021 ◽  
Author(s):  
Marisa Faggini ◽  
Bruna Bruno ◽  
Anna Parziale
Keyword(s):  
Complex System ◽  
Nonlinear Dynamics ◽  
Economic Analysis ◽  
Complex Systems ◽  
Reverse Engineering ◽  
Underlying Mechanism ◽  
Economic Data ◽  
Agent Based ◽  
Economic Agents ◽  
Advantages And Disadvantages

AbstractFollowing the reverse engineering (RE) approach to analyse an economic complex system is to infer how its underlying mechanism works. The main factors that condition the difficulty of RE are the number of variable components in the system and, most importantly, the interdependence of components on one another and nonlinear dynamics. All those aspects characterize the economic complex systems within which economic agents make their choices. Economic complex systems are adopted in RE science, and they could be used to understand, predict and model the dynamics of the complex systems that enable to define and to control the economic environment. With the RE approach, economic data could be used to peek into the internal workings of the economic complex system, providing information about its underling nonlinear dynamics. The idea of this paper arises from the aim to deepen the comprehension of this approach and to highlight the potential implementation of tools and methodologies based on it to treat economic complex systems. An overview of the literature about the RE is presented, by focusing on the definition and on the state of the art of the research, and then we consider two potential tools that could translate the methodological issues of RE by evidencing advantages and disadvantages for economic analysis: the recurrence analysis and the agent-based model (ABM).

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