Non-linear Dynamics and Leadership Emergence

The process by which leaders emerge from leaderless groups is well-documented, but not nearly as well understood. This article describes how non-linear dynamical systems concepts of attractors, bifurcations, and self-organization culminate in a swallowtail catastrophe model for the leadership emergence process, and presents the experimental results that the model has produced thus far for creative problem solving, production, and coordination-intensive groups. Several control variables have been identified that vary in their function depending on what type of group is involved, e.g. creative problem solving, production, and coordination-intensive groups. The exposition includes the relevant statistical strategies that are based on non-linear regression along with some directions for new research questions that can be explored through this non-linear model

Performance analysis with network-enhanced complexities: On fading measurements, event-triggered mechanisms, and cyber attacks

Copyright © 2014 Derui Ding et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Nowadays, the real-world systems are usually subject to various complexities such as parameter uncertainties, time-delays, and nonlinear disturbances. For networked systems, especially large-scale systems such as multiagent systems and systems over sensor networks, the complexities are inevitably enhanced in terms of their degrees or intensities because of the usage of the communication networks. Therefore, it would be interesting to (1) examine how this kind of network-enhanced complexities affects the control or filtering performance; and (2) develop some suitable approaches for controller/filter design problems. In this paper, we aim to survey some recent advances on the performance analysis and synthesis with three sorts of fashionable network-enhanced complexities, namely, fading measurements, event-triggered mechanisms, and attack behaviors of adversaries. First, these three kinds of complexities are introduced in detail according to their engineering backgrounds, dynamical characteristic, and modelling techniques. Then, the developments of the performance analysis and synthesis issues for various networked systems are systematically reviewed. Furthermore, some challenges are illustrated by using a thorough literature review and some possible future research directions are highlighted.This work was supported in part by the National Natural Science Foundation of China under Grants 61134009, 61329301, 61203139, 61374127, and 61374010, the Royal Society of the UK, and the Alexander von Humboldt Foundation of Germany

Towards information based spatiotemporal patterns as a foundation for agent representation in dynamical systems

© 2016 Massachusetts Institute of Technology Published under a Creative Commons Attribution 4.0 International (CC BY 4.0 - https://creativecommons.org/licenses/by/4.0/) license.We present some arguments why existing methods for representing agents fall short in applications crucial to artificial life. Using a thought experiment involving a fictitious dynamical systems model of the biosphere we argue that the metabolism, motility, and the concept of counterfactual variation should be compatible with any agent representation in dynamical systems. We then propose an information-theoretic notion of integrated spatiotemporal patterns which we believe can serve as the basic building block of an agent definition. We argue that these patterns are capable of solving the problems mentioned before. We also test this in some preliminary experiments

Nonlinear Dynamics In Musical Interactions

This thesis examines nonlinear dynamical processes in musical tools, identifying certain roles that they play in creative interactions with existing tools, and investigates the roles they might play in digital tools. Nonlinear dynamical processes are fundamental in the everyday physical world. They lie at the core of many acoustic instruments, playing a particularly significant role in bowed and blown instruments. Two major studies are presented that approach these issues from different perspectives. Firstly a set of comparative studies explore the ways in which musicians engage with systems that do and do not incorporate nonlinear dynamical processes. Secondly, interviews with a range of musicians engaged in contemporary musical practices — particularly free improvisation — are used to investigate the role of nonlinear dynamical processes in instrumental interactions in relation to unpredictability and creative exploration. Evidence is presented demonstrating that nonlinear dynamical processes can be drawn on as resources for exploration over long time periods. An approach to creative interaction that explicitly draws on the properties of nonlinear dynamical processes is uncovered and connected to material-oriented notions of creative processes. Nonlinear dynamics are shown to facilitate a productive ‘‘sweet spot’’ between unpredictability and complexity on the one hand, and detailed, sensitive, deterministic control, coupled with the potential to repeat and develop particular actions on the other. The importance of timing in interactions with nonlinear dynamical processes is highlighted as being significant in creating explorable interactions, particularly close to critical thresholds. A distinction is raised between instantaneous unpredictabilities that emerge from the interaction with the tool (interactional ), and unpredictabilities that result from the unexpected implications of the conjunction of otherwise anticipated elements (combinatorial). While the usefulness of the latter in creative interactions is frequently acknowledged in HCI research, the former is often excluded, or seen as a hinderance or obstruction. Engagements with nonlinear dynamical processes in existing musical instruments and practices provide clear evidence of the utility of both nonlinear dynamics, and interactional surprises more generally, suggesting that they can be of use in other domains where creative exploration is a concern

Creativity as Cognitive design \ud The case of mesoscopic variables in Meta-Structures\ud

Creativity is an open problem which has been differently approached by several disciplines since a long time. In this contribution we consider as creative the constructivist design an observer does on the description levels of complex phenomena, such as the self-organized and emergent ones ( e.g., Bènard rollers, Belousov-Zhabotinsky reactions, flocks, swarms, and more radical cognitive and social emergences). We consider this design as related to the Gestaltian creation of a language fit for representing natural processes and the observer in an integrated way. Organised systems, both artificial and most of the natural ones are designed/ modelled according to a logical closed model which masters all the inter-relation between their constitutive elements, and which can be described by an algorithm or a single formal model. We will show there that logical openness and DYSAM (Dynamical Usage of Models) are the proper tools for those phenomena which cannot be described by algorithms or by a single formal model. The strong correlation between emergence and creativity suggests that an open model is the best way to provide a formal definition of creativity. A specific application relates to the possibility to shape the emergence of Collective Behaviours. Different modelling approaches have been introduced, based on symbolic as well as sub-symbolic rules of interaction to simulate collective phenomena by means of computational emergence. Another approach is based on modelling collective phenomena as sequences of Multiple Systems established by percentages of conceptually interchangeable agents taking on the same roles at different times and different roles at the same time. In the Meta-Structures project we propose to use mesoscopic variables as creative design, invention, good continuity and imitation of the description level. In the project we propose to define the coherence of sequences of Multiple Systems by using the values taken on by the dynamic mesoscopic clusters of its constitutive elements, such as the instantaneous number of elements having, in a flock, the same speed, distance from their nearest neighbours, direction and altitude. In Meta-Structures the collective behaviour’s coherence corresponds, for instance, to the scalar values taken by speed, distance, direction and altitude along time, through statistical strategies of interpolation, quasi-periodicity, levels of ergodicity and their reciprocal relationship. In this case the constructivist role of the observer is considered creative as it relates to neither non-linear replication nor transposition of levels of description and models used for artificial systems, like reductionism. Creativity rather lies in inventing new mesoscopic variables able to identify coherent patterns in complex systems. As it is known, mesoscopic variables represent partial macroscopic properties of a system by using some of the microscopic degrees of freedom possessed by composing elements. Such partial usage of microscopic as well as macroscopic properties allows a kind of Gestaltian continuity and imitation between levels of descriptions for mesoscopic modelling. \ud \u

Mathematical problems for complex networks

Copyright @ 2012 Zidong Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. This article is made available through the Brunel Open Access Publishing Fund.Complex networks do exist in our lives. The brain is a neural network. The global economy is a network of national economies. Computer viruses routinely spread through the Internet. Food-webs, ecosystems, and metabolic pathways can be represented by networks. Energy is distributed through transportation networks in living organisms, man-made infrastructures, and other physical systems. Dynamic behaviors of complex networks, such as stability, periodic oscillation, bifurcation, or even chaos, are ubiquitous in the real world and often reconfigurable. Networks have been studied in the context of dynamical systems in a range of disciplines. However, until recently there has been relatively little work that treats dynamics as a function of network structure, where the states of both the nodes and the edges can change, and the topology of the network itself often evolves in time. Some major problems have not been fully investigated, such as the behavior of stability, synchronization and chaos control for complex networks, as well as their applications in, for example, communication and bioinformatics

The Role of Nonlinear Dynamics in Musicians' Interactions with Digital and Acoustic Musical Instruments

Nonlinear dynamical processes are fundamental to the behaviour of acoustic musical instruments, as is well explored in the case of sound production. However, such processes may have profound and under-explored implications for how musicians interact with instruments. While nonlinear dynamical processes are ubiquitous in acoustic instruments, they are present in digital musical tools only if explicitly implemented. Thus, an important resource with potentially major effects on how musicians interact with acoustic instruments is typically absent in the way musicians interact with digital instruments. 24 interviews with free improvising musicians were conducted to explore the role that nonlinear dynamics play in the participants’ musical practices, and to understand how such processes can afford distinctive methods of creative exploration. Thematic analysis of the interview data is used to demonstrate the potential for nonlinear dynamical processes to provide repeatable, learnable, controllable and explorable interactions, and to establish a vocabulary for exploring nonlinear dynamical interactions. Two related approaches to engaging with nonlinear dynamical behaviours are elaborated: edge-like interaction which involves the creative use of critical thresholds; and deep exploration which involves exploring the virtually unlimited subtleties of a very small control region. The elaboration of these approaches provides an important bridge that connects the concrete descriptions of interaction in musical practices on the one hand, to the more abstract mathematical formulation of nonlinear dynamical systems on the other