Related papers: Symmetry breaking in a globally coupled map of fou…
Motivated by proving the loss of ergodicity in expanding systems of piecewise affine coupled maps with arbitrary number of units, all-to-all coupling and inversion symmetry, we provide ad-hoc substitutes - namely inversion-symmetric maps of…
We study a class of globally coupled maps in the continuum limit, where the individual maps are expanding maps of the circle. The circle maps in question are such that the uncoupled system admits a unique absolutely continuous invariant…
From a dynamical viewpoint, basic phase transitions of statistical mechanics can be regarded as a breaking of ergodicity. While many random models exhibiting such transitions at the thermodynamics limit exist, finite-dimensional examples…
Globally coupled doubling maps are studied in this paper. In this setting and for finitely many sites, two distinct bifurcation values of the coupling strength have been identified in the literature, corresponding to the emergence of…
We introduce a new method for determining the global stability of synchronization in systems of coupled identical maps. The method is based on the study of invariant measures. Besides the simplest non-trivial example, namely two…
Bifurcations in a system of coupled maps are investigated. Using symbolic dynamics it is proven that for coupled shift maps the well known space--time--mixing attractor becomes unstable at a critical coupling strength in favour of a…
Critical points of an invariant function may or may not be symmetric. We prove, however, that if a symmetric critical point exists, those adjacent to it are generically symmetry breaking. This mathematical mechanism is shown to carry…
The coupled (chaotic) map lattices (CMLs) characterizes the collective dynamics of a spatially distributed system consisting of locally or globally coupled maps. The current research on the dynamic behavior of CMLs is based on the framework…
Symmetry plays a crucial role in understanding the properties of mathematical structures and optimization problems. Recent work has explored this phenomenon in the context of neural networks, where the loss function is invariant under…
We study a class of one-dimensional full branch maps admitting two indifferent fixed points as well as critical points and/or unbounded derivative. Under some mild assumptions we prove the existence of a unique invariant mixing absolutely…
The concept of symmetry breaking and the emergence of corresponding local order parameters constitute the pillars of modern day many body physics. The theory of quantum entanglement is currently leading to a paradigm shift in understanding…
For a family of random intermittent dynamical systems with a superattracting fixed point we prove that a phase transition occurs between the existence of an absolutely continuous invariant probability measure and infinite measure depending…
We introduce a dual-core system with double symmetry, one between the cores, and one along each core, imposed by the spatial modulation of local nonlinearity in the form of two tightly localized spots, which may be approximated by a pair of…
A spatially one dimensional coupled map lattice possessing the same symmetries as the Miller Huse model is introduced. Our model is studied analytically by means of a formal perturbation expansion which uses weak coupling and the vicinity…
A random matrix model to describe the coupling of m-fold symmetry in constructed. The particular threefold case is used to analyze data on eigenfrequencies of elastomechanical vibration of an anisotropic quartz block. It is suggested that…
A random matrix model to describe the coupling of $m$-fold symmetry is constructed. The particular threefold case is used to analyze data on eigenfrequencies of elastomechanical vibration of an anisotropic quartz block. It is suggested that…
We investigate the remarkable role of position dependent damping in determining the parametric regions of symmetry breaking in nonlinear $\cal{PT}$-symmetric systems. We illustrate the nature of $\cal{PT}$-symmetry preservation and breaking…
Soft breaking of a symmetry requires an invariance of the dimension-4 part of the Lagrangian and non-trivial variation of the lower-dimensional part. However, in general, separation between the dim-4 and lower-dimensional Lagrangian is not…
Synchronisation between coupled oscillatory systems is a common phenomenon in many natural as well as technical systems. Varying the strength of coupling often leads to qualitative changes in the complex dynamics of the mutually coupled…
Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where…