Asynchronous Networks and Event Driven Dynamics

Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a theoretical and conceptual framework for the study of network dynamics where nodes can evolve independently of one another, be constrained, stop, and later restart, and where the interaction between different components of the network may depend on time, state, and stochastic effects. This framework is sufficiently general to encompass a wide range of applications ranging from engineering to neuroscience. Typically, dynamics is piecewise smooth and there are relationships with Filippov systems. In the first part of the paper, we give examples of asynchronous networks, and describe the basic formalism and structure. In the second part, we make the notion of a functional asynchronous network rigorous, discuss the phenomenon of dynamical locks, and present a foundational result on the spatiotemporal factorization of the dynamics for a large class of functional asynchronous networks

On the emergence of scale-free production networks

We propose a simple dynamical model of the formation of production networks among monopolistically competitive firms. The model subsumes the standard general equilibrium approach \`a la Arrow-Debreu but displays a wide set of potential dynamic behaviors. It robustly reproduces key stylized facts of firms' demographics. Our main result is that competition between intermediate good producers generically leads to the emergence of scale-free production networks.Comment: 31 pages, 15 figure

Design of stable metabolic networks

In this work, we propose eigenvalue optimization combined with Lyapunov theory concepts to ensure stability of the Embden—Meyerhof–Parnas pathway, the pentosephosphate pathway, the phosphotransferase system and fermentation reactions of Escherichia coli. We address the design of a metabolic network for the maximization of different metabolite production rates. The first case study focuses on serine production, based on a model that consists of 18 differential equations corresponding to dynamic mass balances for extracellular glucose and intracellular metabolites, and thirty kinetic rate expressions. A second case study addresses the design problem to maximize ethanol production, based on a dynamic model that involves mass balancesfor 25 metabolites and 38 kinetic rate equations. The nonlinear optimization problem including stability constraints has been solved with reduced space Successive Quadratic Programming techniques. Numerical results provide useful insights on the stability properties of the studied kinetic models.Fil: Di Maggio, Jimena Andrea. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; ArgentinaFil: Blanco, Anibal Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; ArgentinaFil: Bandoni, Jose Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; ArgentinaFil: Diaz Ricci, Juan Carlos. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Tucumán. Instituto Superior de Investigaciones Biológicas. Universidad Nacional de Tucumán. Instituto Superior de Investigaciones Biológicas; ArgentinaFil: Díaz, María Soledad. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; Argentin

Approximation of dynamical systems using S-systems theory : application to biological systems

In this paper we propose a new symbolic-numeric algorithm to find positive equilibria of a n-dimensional dynamical system. This algorithm implies a symbolic manipulation of ODE in order to give a local approximation of differential equations with power-law dynamics (S-systems). A numerical calculus is then needed to converge towards an equilibrium, giving at the same time a S-system approximating the initial system around this equilibrium. This algorithm is applied to a real biological example in 14 dimensions which is a subsystem of a metabolic pathway in Arabidopsis Thaliana

Robust and Irreversible Development in Cell Society as a General Consequence of Intra-Inter Dynamics

A dynamical systems scenario for developmental cell biology is proposed, based on numerical studies of a system with interacting units with internal dynamics and reproduction. Diversification, formation of discrete and recursive types, and rules for differentiation are found as a natural consequence of such a system. "Stem cells" that either proliferate or differentiate to different types stochastically are found to appear when intra-cellular dynamics are chaotic. Robustness of the developmental process against microscopic and macroscopic perturbations is shown to be a natural consequence of such intra-inter dynamics, while irreversibility in developmental process is discussed in terms of the gain of stability, loss of diversity and chaotic instability.Comment: 17 pages with 3 ps figures. submitted to Physica A as a proceeding paperfor Paladin Memorial Con

Effects of energy storage systems grid code requirements on interface protection performances in low voltage networks

The ever-growing penetration of local generation in distribution networks and the large diffusion of energy storage systems (ESSs) foreseen in the near future are bound to affect the effectiveness of interface protection systems (IPSs), with negative impact on the safety of medium voltage (MV) and low voltage (LV) systems. With the scope of preserving the main network stability, international and national grid connection codes have been updated recently. Consequently, distributed generators (DGs) and storage units are increasingly called to provide stabilizing functions according to local voltage and frequency. This can be achieved by suitably controlling the electronic power converters interfacing small-scale generators and storage units to the network. The paper focuses on the regulating functions required to storage units by grid codes currently in force in the European area. Indeed, even if such regulating actions would enable local units in participating to network stability under normal steady-state operating conditions, it is shown through dynamic simulations that they may increase the risk of unintentional islanding occurrence. This means that dangerous operating conditions may arise in LV networks in case dispersed generators and storage systems are present, even if all the end-users are compliant with currently applied connection standards

Tropicalization and tropical equilibration of chemical reactions

Systems biology uses large networks of biochemical reactions to model the functioning of biological cells from the molecular to the cellular scale. The dynamics of dissipative reaction networks with many well separated time scales can be described as a sequence of successive equilibrations of different subsets of variables of the system. Polynomial systems with separation are equilibrated when at least two monomials, of opposite signs, have the same order of magnitude and dominate the others. These equilibrations and the corresponding truncated dynamics, obtained by eliminating the dominated terms, find a natural formulation in tropical analysis and can be used for model reduction.Comment: 13 pages, 1 figure, workshop Tropical-12, Moskow, August 26-31, 2012; in press Contemporary Mathematic

Transcriptional delay stabilizes bistable gene networks

Transcriptional delay can significantly impact the dynamics of gene networks. Here we examine how such delay affects bistable systems. We investigate several stochastic models of bistable gene networks and find that increasing delay dramatically increases the mean residence times near stable states. To explain this, we introduce a non-Markovian, analytically tractable reduced model. The model shows that stabilization is the consequence of an increased number of failed transitions between stable states. Each of the bistable systems that we simulate behaves in this manner