Related papers: Protected chaos in a topological lattice
The most exciting recent development in nonlinear dynamics is realization that chaos can be useful. One application involves "Secure Communication". Two piecewise linear systems with switching nonlinearities have been taken as chaos…
We prove the holding of chaos in the sense of Li-Yorke for a family of four-dimensional discrete dynamical systems that are naturally associated to ODE systems describing coupled oscillators subject to an external non-conservative force,…
Stable chaos is a generalization of the chaotic behaviour exhibited by cellular automata to continuous-variable systems and it owes its name to an underlying irregular and yet linearly stable dynamics. In this review we discuss analogies…
A main objective of topological photonics is the design of disorder-resilient optical devices. Many prospective applications would benefit from nonlinear effects, which not only are naturally present in real systems but also are needed for…
Non-equilibrium driving of biochemical reactions is believed to enable their robust functioning despite the presence of thermal fluctuations and other sources of disorder. Such robust functions include sensory adaptation, enhanced enyzmatic…
We study topological systems with both a chiral and a spatial symmetry which result in an additional spatial chiral symmetry. We distinguish the topologically nontrivial states according to the chiral symmetries protecting them and study…
The research concerns the dynamics of complex autonomous Kauffman networks. The article defines and shows using simulation experiments half-chaotic networks, which exhibit features much more similar to typically modeled systems like a…
The interplay between time scales and structural properties of complex networks of nonlinear oscillators can generate many interesting phenomena, like amplitude death, cluster synchronization, frequency synchronization etc. We study the…
In chaotic deterministic systems, seemingly stochastic behavior is generated by relatively simple, though hidden, organizing rules and structures. Prominent among the tools used to characterize this complexity in 1D and 2D systems are…
Non-Hermitian quantum systems can exhibit unique observables characterizing topologically protected transport in the presence of decay. The topological protection arises from winding numbers associated with non-decaying dark states, which…
Topological edge states are known to emerge in certain quasicrystals. We investigate a topological quasicrystal in the presence of nonlinearity by generalizing the Toda lattice to include modulated periodic hoppings, where the period is…
Adaptive dynamical networks are network systems in which the structure co-evolves and interacts with the dynamical state of the nodes. We study an adaptive dynamical network in which the structure changes on a slower time scale relative to…
Chaotic dynamics, commonly seen in weather systems and fluid turbulence, are characterized by their sensitivity to initial conditions, which makes accurate prediction challenging. Recent approaches have focused on developing data-driven…
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…
We study chaotic synchronization in networks with time-delayed coupling. We introduce the notion of strong and weak chaos, distinguished by the scaling properties of the maximum Lyapunov exponent within the synchronization manifold for…
Equilibrium topological phases are robust against weak static disorder but may break down in the strong disorder regime. Here we explore the stability of the quench-induced emergent dynamical topology in the presence of dynamical noise. We…
Long and stable timescales are often observed in complex biochemical networks, such as in emergent oscillations. How these robust dynamics persist remains unclear, given the many stochastic reactions and shorter time scales demonstrated by…
The structure of interactions in most of animals and human societies can be best represented by complex hierarchical networks. In order to maintain close to optimal functioning both stability and adaptability are necessary. Here we…
In this article we prove that for a diffeomorphism on a compact Riemannian manifold, if there is a nontrival homoclinic class that is not uniformly hyperbolic or the diffeomorphism is a $C^{1+\alpha}$ and there is a hyperbolic ergodic…
Topological photonic systems offer a robust platform for guiding light in the presence of disorder, but their interplay with quantum emitters remains a frontier for realizing strongly correlated quantum states. Here, we explore a…