Modeling the Dynamics of Complex Interaction Systems: From Morphogenesis to Control

Abstract

<jats:p>The aim of this paper is to contribute to the modeling and analysis of complex systems, taking into account the nature of complexity at different stages of the system life-cycle: from its genesis to its evolution. Therefore, some structural aspects of the complexity dynamics are highlighted, leading (i) to implement the morphogenesis of emergent complex network structures, and (ii) to control some synchronization phenomena within complex networks. Specific applications are proposed to illustrate these two aspects, in urban dynamics and in neural networks.</jats:p>

Large time behaviour and synchronization of complex networks of reaction–diffusion systems of FitzHugh–Nagumo type

“…The blue points represent the values obtained numerically, the red curve represents the function g n = 0.046 n − 0.00043. Thus, we obtain heuristically a 1 n law which is common in other areas and highlights the synchronization emergent property, see for example [9,10,11]. Figure 5: Synchronization of a fully linearly connected network of type (49) with n = 3, c(x) = 0 and g 3 = 0.5.…”

Synchronization and Dynamic Consensus of Heterogeneous Networked Systems

“…where the constants ν i are defined in (12). Next, for these equations to be meaningful, we rewrite them in terms of the state x s .…”

“…assumed, but it may also be nonlinear, as in the well-known example of Kuramoto's oscillator model in which case the interconnection is established via sinusoids -see [11], [12], [13]. Other types of nonlinear coupling appear, for instance, in the modelling of neuronal cells -see [14], [15], as well as in social sciences [16].…”

On Distributed Reduced-Order Observer-Based Protocol for Linear Multiagent Consensus under Switching Topology

“…Theorem 10. For the leader-following multiagent systems (3) and (49), whose interconnection topology graphĜ is fixed and has a globally reachable node V 0 , suppose that the parameter matrices , , , , 1 , and 2 in the dynamic protocol (50) are constructed by Steps (1)-(3) of Algorithm 3 and the coupling strength is satisfied as…”

“…Recently, a great number of researchers pay much attention to the coordination control of the multiagent systems, which have various subject background such as biology, physics, mathematics, information science, computer science, and control science in [1][2][3][4]. Consensus problem is one of the most basic problems of the coordination control of the multiagent systems, and the main idea is to design the distributed protocols which enable a group of agents to achieve an agreement on certain quantities of interest.…”