Related papers: Generalized Lorenz Systems Family
We propose that cycle expansions be ordered with respect to stability rather than orbit length for many chaotic systems, particularly those exhibiting crises. This is illustrated with the strong field Lorentz gas, where we obtain…
We study a family of orthogonal polynomials which generalizes a sequence of polynomials considered by L. Carlitz. We show that they are a special case of the Sheffer polynomials and point out some interesting connections with certain…
Using special quasigraded Lie algebras we obtain new hierarchies of integrable nonlinear vector equations admitting zero-curvature representations. Among them the most interesting is extension of the generalized Landau-Lifshitz hierarchy…
We consider the evolution of the unstable periodic orbit structure of coupled chaotic systems. This involves the creation of a complicated set outside of the synchronization manifold (the emergent set). We quantitatively identify a critical…
This article has been withdrawn in 2013. The class of LOTS (linearly ordered topological spaces) contains many important spaces, like the set of real numbers, the set of rational numbers and the ordinals. Such spaces have rich topological…
Recently, an infinite class of holographic generalized complexities was proposed. These gravitational observables display the behavior required to be duals of complexity, in particular, linear growth at late times and switchback effect. In…
The R\"ossler System is one of the best known chaotic dynamical systems, exhibiting a plethora of complex phenomena - and yet, only a few studies tackled its complexity analytically. In this paper we find sufficient conditions for the…
In [LP] we introduced Laurent phenomenon algebras, a generalization of cluster algebras. Here we give an explicit description of Laurent phenomenon algebras with a linear initial seed arising from a graph. In particular, any graph…
Quantized, compact graphs were shown to be excellent paradigms for quantum chaos in bounded systems. Connecting them with leads to infinity we show that they display all the features which characterize scattering systems with an underlying…
We obtain a generalized law of the iterated logarithm for a class of dependent processes with superdiffusive behaviour. Our results apply in particular to the Lorentz gas with infinite horizon.
Nonlinear perturbation of Fuchsian systems are studied in a region including two singularities. It is proved that such systems are generally not analytically equivalent to their linear part (they are not linearizable) and the obstructions…
Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of…
Chaotic systems arise naturally in Statistical Mechanics and in Fluid Dynamics. A paradigm for their modelization are smooth hyperbolic systems. Are there consequences that can be drawn simply by assuming that a system is hyperbolic? here…
The Chua system, the Lorenz system, the Chen system and The L\"u system are chaotic systems that their state space equations is very similar to Haken system which is a nonlinear model of a optical slow-fast system. These Haken-Like Sys-tems…
It is well-known that the equations for a simple fluid can be cast into what is called their Lagrange formulation. We introduce a notion of a generalized Lagrange formulation, which is applicable to a wide variety of systems of partial…
Numerical experiments recently discussed in the literature show that identical nonlinear chaotic systems linked by a common noise term (or signal) may synchronize after a finite time. We study the process of synchronization as function of…
This article introduces the notion of a loose family of Engel structures and shows that two such families are Engel homotopic if and only if they are formally homotopic. This implies a complete h-principle when some auxiliary data is fixed.…
Some characteristics of the Sawada-Kotera Lagrangian system lend themselves to generalization, producing a large class of separable Lagrangian systems with two degrees of freedom.
In this letter, we propose high order layered complex networks. The synchronization is discussed in detail. The relations of synchronization, individual coupling matrices and the intrinsic function of the uncoupled system are given. As…
We present a wide class of differential systems in any dimension that are either integrable or complete integrable. In particular, our result enlarges a known family of planar integrable systems. We give an extensive list of examples that…