Related papers: Scale-free patterns at a saddle-node bifurcation i…
Traffic congestion continues to escalate with urbanization and socioeconomic development, necessitating advanced modeling to understand and mitigate its impacts. In large-scale networks, traffic congestion can be studied using cascade…
Deterministic sandpile models are studied on a cost optimized Barab\'asi-Albert (BA) scale-free network whose nodes are the sites of a square lattice. For the optimized BA network, the sandpile model has the same critical behaviour as the…
The disorder function formalism [Gunaratne et.al., Phys. Rev. E, {\bf 57}, 5146 (1998)]^M is used to show that pattern relaxation in an experiment on a vibrated layer of brass beads^M occurs in three distinct stages. During stage I, all…
We propose a derivative-free saddle-search algorithm designed to locate transition states using only function evaluations. The algorithm employs a nested architecture consisting of an inner eigenvector search and an outer saddle-point…
Conserved quantities are obtained and analyzed in the new models with global scale invariance recently proposed. Such models allow for non tivial scalar field potentials and masses for particles, so that the scale symmetry must be broken…
We consider the scalar delay differential equation $$ \dot{x}(t)=-x(t)+f_{K}(x(t-1)) $$ with a nondecreasing feedback function $f_{K}$ depending on a parameter $K$, and we verify that a saddle-node bifurcation of periodic orbits takes place…
We consider a stochastic environment with two time scales and outline a general theory that compares two methods to reduce the dimension of the original system. The first method involves the computation of the underlying deterministic…
A topological bifurcation in chaotic scattering is characterized by a sudden change in the topology of the infinite set of unstable periodic orbits embedded in the underlying chaotic invariant set. We uncover a scaling law for the fractal…
We analyze the phenomenon of system size stochastic resonance in a simple spatially extended system by exploiting the knowledge of the nonequilibrium potential. We show that through the analysis of that potential, and particularly its…
We study a random walk problem on the hierarchical network which is a scale-free network grown deterministically. The random walk problem is mapped onto a dynamical Ising spin chain system in one dimension with a nonlocal spin update rule,…
We study the dynamics of generic unfoldings of saddle-node circle local diffeomorphisms from the measure theoretical point of view, obtaining statistical stability results for deterministic and random perturbations in these kind of…
Given a finite set of data generated by an unknown ordinary differential equation it is impossible to exactly determine the associated vector field, and hence, bifurcation theory tells us that it is impossible, in general, to correctly…
Computer simulations of first-order relaxation processes show that the spatial configurations of the system acquire an invariant shape once the stationary regime is attained. Inspired by them we find that, in any first-order relaxation…
In a recursive way and by including a parameter, we introduce a family of deterministic scale-free networks. The resulting networks exhibit small-world effects. We calculate the exact results for the degree exponent, the clustering…
We present a phenomenological description of the critical slowing down associated with period-doubling bifurcations in discrete dynamical systems. Starting from a local Taylor expansion around the fixed point and the bifurcation parameter,…
Symmetries represent a fundamental constraint for physical systems and relevant new phenomena often emerge as a consequence of their breaking. An important example is provided by space- and time-translational invariance in statistical…
A parabolic stochastic PDE is studied analytically and numerically, when a bifurcation parameter is slowly increased through its critical value. The aim is to understand the effect of noise on delayed bifurcations in systems with spatial…
We consider gradient systems with an increasing potential that depends on a scalar parameter. As the parameter is varied, critical points of the potential can be eliminated or created through saddle-node bifurcations causing the system to…
Simulations of a stochastic fixed-energy sandpile in one and two dimensions reveal slow relaxation of the order parameter, even far from the critical point. The decay of the activity is best described by a stretched-exponential form. The…
The approach to equilibrium, from a nonequilibrium initial state, in a system at its critical point is usually described by a scaling theory with a single growing length scale, $\xi(t) \sim t^{1/z}$, where z is the dynamic exponent that…