arXiv subjects

Celso Grebogi

Publications and source records attributed to Celso Grebogi.

At least 55 records · Page 3Linked to original sources

arXiv2013

Resiliently evolving supply-demand networks

The ability to design a transport network such that commodities are brought from suppliers to consumers in a steady, optimal, and stable way is of great importance for nowadays distribution systems. In this Letter, by using the circuit laws of Kirchhoff and Ohm, we provide the exact capacities of the edges that an optimal supply-demand network should have to operate stably under perturbations. The perturbations we consider are the evolution of the connecting topology, the decentralisation of hub sources or sinks, and the intermittence of suppliers/consumers characteristics. We analyse these conditions and the impact of our results, both on the current UK power-grid structure and on numerically generated evolving archetypal network topologies.

physics.soc-ph↗

arXiv2013

Structure and function in flow networks

This Letter presents a unified approach for the fundamental relationship between structure and function in flow networks by solving analytically the voltages in a resistor network, transforming the network structure to an effective all-to-all topology, and then measuring the resultant flows. Moreover, it defines a way to study the structural resilience of the graph and to detect possible communities.

physics.soc-ph↗

arXiv2011

Controllability of Complex Networks with Nonlinear Dynamics

Sun et al. provided an insightful comment arXiv:1108.5739v1 on our manuscript entitled "Controllability of Complex Networks with Nonlinear Dynamics" on arXiv. We agree on their main point that linearization about locally desired states can be violated in general by the breakdown of local control of the linearized complex network with nonlinear state. Therefore, we withdraw our manuscript. However, other than nonlinear dynamics, our claim that a single-node-control can fully control the general bidirectional/undirected linear network with 1D self-dynamics is still valid, which is similar to (but different from) the conclusion of arXiv:1106.2573v3 that all-node-control with a single signal can fully control any direct linear network with nodal-dynamics (1D self-dynamics).

cond-mat.dis-nn↗

arXiv2011

Predicting catastrophes in nonlinear dynamical systems by compressive sensing

An extremely challenging problem of significant interest is to predict catastrophes in advance of their occurrences. We present a general approach to predicting catastrophes in nonlinear dynamical systems under the assumption that the system equations are completely unknown and only time series reflecting the evolution of the dynamical variables of the system are available. Our idea is to expand the vector field or map of the underlying system into a suitable function series and then to use the compressive-sensing technique to accurately estimate the various terms in the expansion. Examples using paradigmatic chaotic systems are provided to demonstrate our idea.

physics.data-an↗

arXiv2011

Collective response of self-organised clusters of mechanosensitive channels

Mechanosensitive channels are ion channels activated by membrane tension. We investigate the influence of bacterial mechanosensitive channels spatial distribution on activation (gating). Based on elastic short-range interactions we map this physical process onto an Ising-like model, which enables us to predict the clustering of channels and the effects of clustering on their gating. We conclude that the aggregation of channels and the consequent interactions among them leads to a global cooperative gating behaviour with potentially dramatic consequences for the cell.

physics.bio-ph↗

arXiv2010

Escape from attracting sets in randomly perturbed systems

The dynamics of escape from an attractive state due to random perturbations is of central interest to many areas in science. Previous studies of escape in chaotic systems have rather focused on the case of unbounded noise, usually assumed to have Gaussian distribution. In this paper, we address the problem of escape induced by bounded noise. We show that the dynamics of escape from an attractor's basin is equivalent to that of a closed system with an appropriately chosen "hole". Using this equivalence, we show that there is a minimum noise amplitude above which escape takes place, and we derive analytical expressions for the scaling of the escape rate with noise amplitude near the escape transition. We verify our analytical predictions through numerical simulations of a two-dimensional map with noise.

nlin.CD↗

arXiv2010

Random fluctuation leads to forbidden escape of particles

A great number of physical processes are described within the context of Hamiltonian scattering. Previous studies have rather been focused on trajectories starting outside invariant structures, since the ones starting inside are expected to stay trapped there forever. This is true though only for the deterministic case. We show however that, under finitely small random fluctuations of the field, trajectories starting inside Arnold-Kolmogorov-Moser (KAM) islands escape within finite time. The non-hyperbolic dynamics gains then hyperbolic characteristics due to the effect of the random perturbed field. As a consequence, trajectories which are started inside KAM curves escape with hyperbolic-like time decay distribution, and the fractal dimension of a set of particles that remain in the scattering region approaches that for hyperbolic systems. We show a universal quadratic power law relating the exponential decay to the amplitude of noise. We present a random walk model to relate this distribution to the amplitude of noise, and investigate this phenomena with a numerical study applying random maps.

nlin.CD↗

arXiv2009

Periodic orbit analysis at the onset of the unstable dimension variability and at the blowout bifurcation

Many chaotic dynamical systems of physical interest present a strong form of nonhyperbolicity called unstable dimension variability (UDV), for which the chaotic invariant set contains periodic orbits possessing different numbers of unstable eigendirections. The onset of UDV is usually related to the loss of transversal stability of an unstable fixed point embedded in the chaotic set. In this paper, we present a new mechanism for the onset of UDV, whereby the period of the unstable orbits losing transversal stability tends to infinity as we approach the onset of UDV. This mechanism is unveiled by means of a periodic orbit analysis of the invariant chaotic attractor for two model dynamical systems with phase spaces of low dimensionality, and seems to depend heavily on the chaotic dynamics in the invariant set. We also described, for these systems, the blowout bifurcation (for which the chaotic set as a whole loses transversal stability) and its relation with the situation where the effects of UDV are the most intense. For the latter point, we found that chaotic trajectories off, but very close to, the invariant set exhibit the same scaling characteristic of the so-called on-off intermittency.

nlin.CD↗

arXiv2009

Emerging attractors and the transition from dissipative to conservative dynamics

The topological structure of basin boundaries plays a fundamental role in the sensitivity to the initial conditions in chaotic dynamical systems. Herewith we present a study on the dynamics of dissipative systems close to the Hamiltonian limit, emphasising the increasing number of periodic attractors and on the structural changes in their basin boundaries as the dissipation approaches zero. We show numerically that a power law with nontrivial exponent describes the growth of the total number of periodic attractors as the damping is decreased. We also establish that for small scales the dynamics is governed by \emph{effective} dynamical invariants, whose measure depends not only on the region of the phase space, but also on the scale under consideration. Therefore, our results show that the concept of effective invariants is also relevant for dissipative systems.

nlin.CD↗

arXiv2007

Signatures of fractal clustering of aerosols advected under gravity

Aerosols under chaotic advection often approach a strange attractor. They move chaotically on this fractal set but, in the presence of gravity, they have a net vertical motion downwards. In practical situations, observational data may be available only at a given level, for example at the ground level. We uncover two fractal signatures of chaotic advection of aerosols under the action of gravity. Each one enables the computation of the fractal dimension $D_{0}$ of the strange attractor governing the advection dynamics from data obtained solely at a given level. We illustrate our theoretical findings with a numerical experiment and discuss their possible relevance to meteorology.

nlin.CD↗

arXiv2007

The multifractal fly: a dynamically multilayered visual system

We dynamically analyze our experimental results on the motion sensitive spiking H1 neuron of the fly's visual system. We find that the fly uses an alphabet composed of a few letters to encode the information contained in the stimulus. The {\em alphabet dynamics} is multifractal both with and without stimulus, though the multifractality increases with the stimulus entropy. This is in sharp contrast to models generating independent spike-intervals, whose dynamics is monofractal.

q-bio.NC↗

arXiv2005

Finite-size effects on open chaotic advection

We study the effects of finite-sizeness on small, neutrally buoyant, spherical particles advected by open chaotic flows. We show that, when projected onto configuration space, the advected finite-size particles disperse about the unstable manifold of the chaotic saddle that governs the passive advection. Using a discrete-time system for the dynamics, we obtain an expression predicting the dispersion of the finite-size particles in terms of their Stokes parameter at the onset of the finite-sizeness induced dispersion. We test our theory in a system derived from a flow and find remarkable agreement between our expression and the numerically measured dispersion.

nlin.CD↗

arXiv2005

Effective dynamics in Hamiltonian systems with mixed phase space

An adequate characterization of the dynamics of Hamiltonian systems at physically relevant scales has been largely lacking. Here we investigate this fundamental problem and we show that the finite-scale Hamiltonian dynamics is governed by effective dynamical invariants, which are significantly different from the dynamical invariants that describe the asymptotic Hamiltonian dynamics. The effective invariants depend both on the scale of resolution and the region of the phase space under consideration, and they are naturally interpreted within a framework in which the nonhyperbolic dynamics of the Hamiltonian system is modeled as a chain of hyperbolic systems.

nlin.CD↗

arXiv2004

Poincare recurrence and measure of hyperbolic and nonhyperbolic chaotic attractors

We study Poincare recurrence of chaotic attractors for regions of finite size. Contrary to the standard case, where the size of the recurrent regions tends to zero, the measure is not supported anymore solely by unstable periodic orbits inside it, but also by other special recurrent trajectories, located outside that region. The presence of the latter leads to a deviation of the distribution of the Poincare first return times from a Poissonian. Consequently, by taken into account the contribution of these recurrent trajectories, a corrected estimate of the measure can be provided. This has wide experimental implications, as in the laboratory all returns can exclusively be observed for regions of finite size only.

nlin.CD↗

arXiv2004

Escaping from nonhyperbolic chaotic attractors

We study the noise-induced escape process from chaotic attractors in nonhyperbolic systems. We provide a general mechanism of escape in the low noise limit, employing the theory of large fluctuations. Specifically, this is achieved by solving the variational equations of the auxiliary Hamiltonian system and by incorporating the initial conditions on the chaotic attractor unambiguously. Our results are exemplified with the H{é}non and the Ikeda map and can be implemented straightforwardly to experimental data.

nlin.CD↗

arXiv2004

Stability Properties of Nonhyperbolic Chaotic Attractors under Noise

We study local and global stability of nonhyperbolic chaotic attractors contaminated by noise. The former is given by the maximum distance of a noisy trajectory from the noisefree attractor, while the latter is provided by the minimal escape energy necessary to leave the basin of attraction, calculated with the Hamiltonian theory of large fluctuations. We establish the important and counterintuitive result that both concepts may be opposed to each other. Even when one attractor is globally more stable than another one, it can be locally less stable. Our results are exemplified with the Holmes map, for two different sets of parameter, and with a juxtaposition of the Holmes and the Ikeda maps. Finally, the experimental relevance of these findings is pointed out.

nlin.CD↗

arXiv2004

Universality in active chaos

Many examples of chemical and biological processes take place in large-scale environmental flows. Such flows generate filamental patterns which are often fractal due to the presence of chaos in the underlying advection dynamics. In such processes, hydrodynamical stirring strongly couples into the reactivity of the advected species and might thus make the traditional treatment of the problem through partial differential equations difficult. Here we present a simple approach for the activity in in-homogeneously stirred flows. We show that the fractal patterns serving as skeletons and catalysts lead to a rate equation with a universal form that is independent of the flow, of the particle properties, and of the details of the active process. One aspect of the universality of our appraoch is that it also applies to reactions among particles of finite size (so-called inertial particles).

nlin.CD↗

arXiv2003

Reactive dynamics of inertial particles in nonhyperbolic chaotic flows

Anomalous kinetics of infective (e.g., autocatalytic) reactions in open, nonhyperbolic chaotic flows are important for many applications in biological, chemical, and environmental sciences. We present a scaling theory for the singular enhancement of the production caused by the universal, underlying fractal patterns. The key dynamical invariant quantities are the effective fractal dimension and effective escape rate, which are primarily determined by the hyperbolic components of the underlying dynamical invariant sets. The theory is general as it includes all previously studied hyperbolic reactive dynamics as a special case. We introduce a class of dissipative embedding maps for numerical verification.

nlin.CD↗