arXiv subjects

Jason Hindes

Publications and source records attributed to Jason Hindes.

28 records · Page 2Linked to original sources

arXiv2019

Network desynchronization by non-Gaussian fluctuations

Many networks must maintain synchrony despite the fact that they operate in noisy environments. Important examples are stochastic inertial oscillators, which are known to exhibit fluctuations with broad tails in many applications, including electric power networks with renewable energy sources. Such non-Gaussian fluctuations can result in rare network desynchronization. Here we build a general theory for inertial oscillator network desynchronization by non-Gaussian noise. We compute the rate of desynchronization and show that higher-moments of noise enter at specific powers of coupling: either speeding up or slowing down the rate exponentially depending on how noise statistics match the statistics of a network's slowest mode. Finally, we use our theory to introduce a technique that drastically reduces the effective description of network desynchronization. Most interestingly, when instability is associated with a single edge, the reduction is to one stochastic oscillator.

nlin.AO↗

arXiv2019

Degree Dispersion Increases the Rate of Rare Events in Population Networks

There is great interest in predicting rare and extreme events in complex systems, and in particular, understanding the role of network topology in facilitating such events. In this work, we show that degree dispersion -- the fact that the number of local connections in networks varies broadly -- increases the probability of large, rare fluctuations in population networks generically. We perform explicit calculations for two canonical and distinct classes of rare events: network extinction and switching. When the distance to threshold is held constant, and hence stochastic effects are fairly compared among networks, we show that there is a universal, exponential increase in the rate of rare events proportional to the variance of a network's degree distribution over its mean squared.

cond-mat.stat-mech↗

arXiv2018

Rare slips in fluctuating synchronized oscillator networks

We study rare phase slips due to noise in synchronized Kuramoto oscillator networks. In the small-noise limit, we demonstrate that slips occur via large fluctuations to saddle phase-locked states. For tree topologies, slips appear between subgraphs that become disconnected at a saddle-node bifurcation, where phase-locked states lose stability generically. This pattern is demonstrated for sparse networks with several examples. Scaling laws are derived and compared for different tree topologies. On the other hand, for dense networks slips occur between oscillators on the edges of the frequency distribution. If the distribution is discrete, the probability-exponent for large fluctuations to occur scales linearly with the system size. However, if the distribution is continuous, the probability is a constant in the large network limit, as individual oscillators fluctuate to saddles while all others remain fixed. In the latter case, the network's coherence is approximately preserved.

cond-mat.dis-nn↗

arXiv2018

Enhancement of large fluctuations to extinction in adaptive networks

During an epidemic, individual nodes in a network may adapt their connections to reduce the chance of infection. A common form of adaption is avoidance rewiring, where a noninfected node breaks a connection to an infected neighbor and forms a new connection to another noninfected node. Here we explore the effects of such adaptivity on stochastic fluctuations in the susceptible-infected-susceptible model, focusing on the largest fluctuations that result in extinction of infection. Using techniques from large-deviation theory, combined with a measurement of heterogeneity in the susceptible degree distribution at the endemic state, we are able to predict and analyze large fluctuations and extinction in adaptive networks. We find that in the limit of small rewiring there is a sharp exponential reduction in mean extinction times compared to the case of zero adaption. Furthermore, we find an exponential enhancement in the probability of large fluctuations with increased rewiring rate, even when holding the average number of infected nodes constant.

nlin.AO↗

arXiv2017

Large order fluctuations, switching, and control in complex networks

We propose an analytical technique to study large fluctuations and switching from internal noise in complex networks. Using order-disorder kinetics as a generic example, we construct and analyze the most probable, or optimal path of fluctuations from one ordered state to another in real and synthetic networks. The method allows us to compute the distribution of large fluctuations and the time scale associated with switching between ordered states for networks consistent with mean-field assumptions. In general, we quantify how network heterogeneity influences the scaling patterns and probabilities of fluctuations. For instance, we find that the probability of a large fluctuation near an order-disorder transition decreases exponentially with the participation ratio of a network's principle eigenvector -- measuring how many nodes effectively contribute to an ordered state. Finally, the proposed theory is used to answer how and where a network should be targeted in order to optimize the time needed to observe a switch.

physics.soc-ph↗

arXiv2017

Epidemic Extinction Paths in Complex Networks

We study the extinction of long-lived epidemics on finite complex networks induced by intrinsic noise. Applying analytical techniques to the stochastic Susceptible-Infected-Susceptible model, we predict the distribution of large fluctuations, the most probable, or optimal path through a network that leads to a disease-free state from an endemic state, and the average extinction time in general configurations. Our predictions agree with Monte-Carlo simulations on several networks, including synthetic weighted and degree-distributed networks with degree correlations, and an empirical high school contact network. In addition, our approach quantifies characteristic scaling patterns for the optimal path and distribution of large fluctuations, both near and away from the epidemic threshold, in networks with heterogeneous eigenvector centrality and degree distributions.

physics.soc-ph↗

arXiv2016

Epidemic extinction and control in heterogeneous networks

We consider epidemic extinction in finite networks with broad variation in local connectivity. Generalizing the theory of large fluctuations to random networks with a given degree distribution, we are able to predict the most probable, or optimal, paths to extinction in various configurations, including truncated power-laws. We find that paths for heterogeneous networks follow a limiting form in which infection first decreases in low-degree nodes, which triggers a rapid extinction in high- degree nodes, and finishes with a residual low-degree extinction. The usefulness of the approach is further demonstrated through optimal control strategies that leverage finite-size fluctuations. Interestingly, we find that the optimal control is a mix of treating both high and low-degree nodes based on large-fluctuation theoretical predictions.

nlin.AO↗

arXiv2016

Hybrid dynamics in delay-coupled swarms with "mothership" networks

Swarming behavior continues to be a subject of immense interest because of its centrality in many naturally occurring systems in physics and biology, as well as its importance in applications such as robotics. Here we examine the effects on swarm pattern formation from delayed communication and topological heterogeneity, and in particular, the inclusion of a relatively small number of highly connected nodes, or "motherships", in a swarm's communication network. We find generalized forms of basic patterns for networks with general degree distributions, and a variety of new behaviors including new parameter regions with multi-stability and hybrid motions in bimodal networks. The latter is an interesting example of how heterogeneous networks can have dynamics that is a mix of different states in homogeneous networks, where high and low-degree nodes have simultaneously distinct behavior.

nlin.AO↗

arXiv2015

Driven synchronization in random networks of oscillators

Synchronization is a universal phenomenon found in many non-equilibrium systems. Much recent interest in this area has overlapped with the study of complex networks, where a major focus is determining how a system's connectivity patterns affect the types of behavior that it can produce. Thus far, modeling efforts have focused on the tendency of networks of oscillators to mutually synchronize themselves, with less emphasis on the effects of external driving. In this work we discuss the interplay between mutual and driven synchronization in networks of phase oscillators of the Kuramoto type, and explore how the structure and emergence of such states depends on the underlying network topology for simple random networks with a given degree distribution. We find a variety of interesting dynamical behaviors, including bifurcations and bistability patterns that are qualitatively different for heterogeneous and homogeneous networks, and which are separated by a Takens-Bogdanov-Cusp singularity in the parameter region where the coupling strength between oscillators is weak. Our analysis is connected to the underlying dynamics of oscillator clusters for important states and transitions.

nlin.AO↗

arXiv2013

Epidemic fronts in complex networks with metapopulation structure

Infection dynamics have been studied extensively on complex networks, yielding insight into the effects of heterogeneity in contact patterns on disease spread. Somewhat separately, metapopulations have provided a paradigm for modeling systems with spatially extended and "patchy" organization. In this paper we expand on the use of multitype networks for combining these paradigms, such that simple contagion models can include complexity in the agent interactions and multiscale structure. We first present a generalization of the Volz-Miller mean-field approximation for Susceptible-Infected-Recovered (SIR) dynamics on multitype networks. We then use this technique to study the special case of epidemic fronts propagating on a one-dimensional lattice of interconnected networks - representing a simple chain of coupled population centers - as a necessary first step in understanding how macro-scale disease spread depends on micro-scale topology. Using the formalism of front propagation into unstable states, we derive the effective transport coefficients of the linear spreading: asymptotic speed, characteristic wavelength, and diffusion coefficient for the leading edge of the pulled fronts, and analyze their dependence on the underlying graph structure. We also derive the epidemic threshold for the system and study the front profile for various network configurations. To our knowledge, this is the first such application of front propagation concepts to random network models.

physics.soc-ph↗