1,840 research outputs found
Synchronizing noisy nonidentical oscillators by transient uncoupling
Synchronization is the process of achieving identical dynamics among coupled
identical units. If the units are different from each other, their dynamics
cannot become identical; yet, after transients, there may emerge a functional
relationship between them -- a phenomenon termed "generalized synchronization."
Here, we show that the concept of transient uncoupling, recently introduced for
synchronizing identical units, also supports generalized synchronization among
nonidentical chaotic units. Generalized synchronization can be achieved by
transient uncoupling even when it is impossible by regular coupling. We
furthermore demonstrate that transient uncoupling stabilizes synchronization in
the presence of common noise. Transient uncoupling works best if the units stay
uncoupled whenever the driven orbit visits regions that are locally diverging
in its phase space. Thus, to select a favorable uncoupling region, we propose
an intuitive method that measures the local divergence at the phase points of
the driven unit's trajectory by linearizing the flow and subsequently
suppresses the divergence by uncoupling
Quantifying Transient Spreading Dynamics on Networks
Spreading phenomena on networks are essential for the collective dynamics of
various natural and technological systems, from information spreading in gene
regulatory networks to neural circuits or from epidemics to supply networks
experiencing perturbations. Still, how local disturbances spread across
networks is not yet quantitatively understood. Here we analyze generic
spreading dynamics in deterministic network dynamical systems close to a given
operating point. Standard dynamical systems' theory does not explicitly provide
measures for arrival times and amplitudes of a transient, spreading signal
because it focuses on invariant sets, invariant measures and other quantities
less relevant for transient behavior. We here change the perspective and
introduce effective expectation values for deterministic dynamics to work out a
theory explicitly quantifying when and how strongly a perturbation initiated at
one unit of a network impacts any other. The theory provides explicit timing
and amplitude information as a function of the relative position of initially
perturbed and responding unit as well as on the entire network topology.Comment: 9 pages and 4 figures main manuscript 9 pages and 3 figures appendi
Controlling percolation with limited resources
Connectivity - or the lack thereof - is crucial for the function of many
man-made systems, from financial and economic networks over epidemic spreading
in social networks to technical infrastructure. Often, connections are
deliberately established or removed to induce, maintain, or destroy global
connectivity. Thus, there has been a great interest in understanding how to
control percolation, the transition to large-scale connectivity. Previous work,
however, studied control strategies assuming unlimited resources. Here, we
depart from this unrealistic assumption and consider the effect of limited
resources on the effectiveness of control. We show that, even for scarce
resources, percolation can be controlled with an efficient intervention
strategy. We derive this strategy and study its implications, revealing a
discontinuous transition as an unintended side-effect of optimal control.Comment: 5 pages, 4 figures, additional supplemental material (19 pages
Transient Uncoupling Induces Synchronization
Finding conditions that support synchronization is a fertile and active area
of research with applications across multiple disciplines. Here we present and
analyze a scheme for synchronizing chaotic dynamical systems by transiently
uncoupling them. Specifically, systems coupled only in a fraction of their
state space may synchronize even if fully coupled they do not. Although, for
many standard systems, coupling strengths need to be bounded to ensure
synchrony, transient uncoupling removes this bound and thus enables
synchronization in an infinite range of effective coupling strengths. The
presented coupling scheme thus opens up the possibility to induce synchrony in
(biological or technical) systems whose parameters are fixed and cannot be
modified continuously.Comment: 5 pages, 6 figure
Exponential Adoption of Battery Electric Cars
The adoption of battery electric vehicles (BEVs) may significantly reduce
greenhouse gas emissions caused by road transport. However, there is wide
disagreement as to how soon battery electric vehicles will play a major role in
overall transportation. Focusing on battery electric passenger cars, we here
analyze BEV adoption across 17 individual countries, Europe, and the World, and
consistently find exponential growth trends. Modeling-based estimates of future
adoption given past trends suggests system-wide adoption substantially faster
than typical economic analyses have proposed so far. For instance, we estimate
the majority of passenger cars in Europe to be electric by about 2031. Within
regions, the predicted times of mass adoption are largely insensitive to model
details. Despite significant differences in current electric fleet sizes across
regions, their growth rates consistently indicate fast doubling times of
approximately 15 months, hinting at radical economic and infrastructural
consequences in the near future
Adhesion-induced Discontinuous Transitions and Classifying Social Networks
Transition points mark qualitative changes in the macroscopic properties of
large complex systems. Explosive transitions, exhibiting properties of both
continuous and discontinuous phase transitions, have recently been uncovered in
network growth processes. Real networks not only grow but often also
restructure, yet common network restructuring processes, such as small world
rewiring, do not exhibit phase transitions. Here, we uncover a class of
intrinsically discontinuous transitions emerging in network restructuring
processes controlled by \emph{adhesion} -- the preference of a chosen link to
remain connected to its end node. Deriving a master equation for the temporal
network evolution and working out an analytic solution, we identify genuinely
discontinuous transitions in non-growing networks, separating qualitatively
distinct phases with monotonic and with peaked degree distributions.
Intriguingly, our analysis of heuristic data indicates a separation between the
same two forms of degree distributions distinguishing abstract from
face-to-face social networks.Comment: 6 pages incl. references, accepted at Physical Review Letter
Network Formation and Dynamics under Economic Constraints
Networks describe a broad range of systems across a wide variety of topics from social and economic interactions over technical infrastructures such as power grids and the internet to biological contexts such as food webs or neural networks. A number of large scale failures and events in these interconnected systems in recent years has shown that understanding the behavior of individual units of these networks is not necessarily sufficient to handle the increasing complexity of these systems. Many theoretical models have been studied to understand the fundamental mechanisms underlying the formation and function of networked systems and a general framework was developed to describe and understand networked systems. However, most of these models ignore a constraint that affects almost all realistic systems: limited resources. In this thesis I study the effects of economic constraints, such as a limited budget or cost minimization, both on the control of network formation and dynamics as well as on network formation itself. I introduce and analyze a new coupling scheme for coupled dynamical systems, showing that synchronization of chaotic units can be enhanced by restricting the interactions based on the states of the individual units, thus saving interactions costs. This new interaction scheme guarantees synchronizability of arbitrary networks of coupled chaotic oscillators, independent of the network topology even with strongly limited interactions. I then propose a new order parameter to measure the degree of phase coherence of networks of coupled phase oscillators. This new order parameter accurately describes the phase coherence in all stages of incoherent movement, partial and full phase locking up to full synchrony. Importantly, I analytically relate this order parameter directly to the stability of the phase locked state. In the second part, I consider the formation of networks under economic constraints from two different points of view. First I study the effects of explicitly limited resources on the control of random percolation, showing that optimal control can have undesired side effects. Specifically, maximal delay of percolation with a limited budget results in a discontinuous percolation transition, making the transition itself uncontrollable in the sense that a single link can have a macroscopic effect on the connectivity. Finally, I propose a model where network formation is driven by cost minimization of the individual nodes in the network. Based on a simple economically motivated supply problem, the resulting network structure is given as the solution of a large number of individual but interaction optimization problem. I show that these network states directly correspond to the final states of a local percolation algorithm and analyze the effects of local optimization on the network formation process.
Overall, I reveal mechanisms and phenomena introduced by these economic constraints that are typically not considered in the standard models, showing that economic constraints can strongly alter the formation and function of networked systems. Thereby, I extend the theoretical understanding that we have of networked systems to economic considerations. I hope that this thesis enables better prediction and control networked systems in realistic settings
- …