Related papers: Instability of Renormalization
The critical behavior for intermittency is studied in two coupled one-dimensional (1D) maps. We find two fixed maps of an approximate renormalization operator in the space of coupled maps. Each fixed map has a common relavant eigenvaule…
We study a one-parameter family of time-reversible Hamiltonian vector fields in $\mathbb{R}^4$, which has received great attention in the literature. On the one hand, it is due to the role it plays in the context of certain applications in…
We develop a theory for thermodynamic instabilities of complex fluids composed of many interacting chemical species organised in families. This model includes partially structured and partially random interactions and can be solved exactly…
The problem of renormalization of the semiclassical one-loop equations used in the non-equilibrium field theory is considered. Recently, the renormalizability of such equations has been justified for some special cases of classical field…
The dynamic instability of the living systems and the "superposition" of different forms of randomness are viewed as a component of the contingently increasing organization of life along evolution. We briefly survey how classical and…
The theory of complex networks and of disordered systems is used to study the stability and dynamical properties of a simple model of material flow networks defined on random graphs. In particular we address instabilities that are…
In this work we suggest that a turbulent phase of the Rayleigh-Taylor instability can be explained as a universal stochastic wave traveling with constant speed in a properly renormalized system. This wave, originating from ordinary…
We study the topological properties of one dimensional systems undergoing unitary time evolution. We show that symmetries possessed both by the initial wavefunction and by the Hamiltonian at all times may not be present in the…
Gibbs' phase rule states that two-phase coexistence of a single-component system, characterized by an n-dimensional parameter-space, may occur in an n-1-dimensional region. For example, the two equilibrium phases of the Ising model coexist…
It is shown that classical spaces with geometries emerge on boundaries of randomly connected tensor networks with appropriately chosen tensors in the thermodynamic limit. With variation of the tensors, the dimensions of the spaces can be…
Biological systems rely on robust internal information processing: Survival depends on highly reproducible dynamics of regulatory processes. Biological information processing elements, however, are intrinsically noisy (genetic switches,…
It is shown that some topological equivalency classes of S-unimodal maps are equal to quasisymmetric conjugacy classes. This includes some infinitely renormalizable polynomials of unbounded type.
The apparent stability of population oscillations in ecological systems is a long-standing puzzle. A generic solution for this problem is suggested here. The stabilizing mechanism involves the combined effect of spatial migration,…
We describe a simple adaptive network of coupled chaotic maps. The network reaches a stationary state (frozen topology) for all values of the coupling parameter, although the dynamics of the maps at the nodes of the network can be…
Complex dynamical systems are often modeled as networks, with nodes representing dynamical units which interact through the network's links. Gene regulatory networks, responsible for the production of proteins inside a cell, are an example…
We generalise a fundamental graph-theoretical fact, stating that every element of the cycle space of a graph is a sum of edge-disjoint cycles, to arbitrary continua. To achieve this we replace graph cycles by topological circles, and…
Rhythmic activities that alternate between coherent and incoherent phases are ubiquitous in chemical, ecological, climate, or neural systems. Despite their importance, general mechanisms for their emergence are little understood. In order…
Networks are a widely used and efficient paradigm to model real-world systems where basic units interact pairwise. Many body interactions are often at play, and cannot be modelled by resorting to binary exchanges. In this work, we consider…
Using the relativistic concept of time dilation we show that a superposition of gravitational potentials can lead to nonunitary time evolution. For sufficiently weak gravitational potentials one can still define, for all intents and…
Cycling chaos is a heteroclinic connection between several chaotic attractors, at which switching between the chaotic sets occur at growing time intervals. Here we characterize the coherence properties of these switchings, considering…