We compute the exact rates of convergence in total variation associated with the ‘fourth moment theorem’ by Nualart and Peccati (2005), stating that a sequence of random variables living in a fixed Wiener chaos verifies a central limit theorem (CLT) if and only if the sequence of the corresponding fourth cumulants converges to zero. We also provide an explicit illustration based on the Breuer-M...

Collective chaos is shown to emerge, via a period-doubling cascade, from quasiperiodic partial synchronization in a population of identical inhibitory neurons with delayed global coupling. This system is thoroughly investigated by means of an exact model of the macroscopic dynamics, valid in the thermodynamic limit. The collective chaotic state is reproduced numerically with a finite population...

The response of weakly disordered metallic grains to Aharonov-Bohm ux suggests a rescaling in which statistical correlators become universal. We derive an exact expression for a correlator of level \velocities," and provide numerical evidence which suggests that the universality extends to a wider class of systems and generalizes to arbitrary perturbations providing a new characterization of qu...

In UWB systems three factors have to be considered to design a radio link: (i) peakand (ii) average power limits defined by FCC Regulations and (iii) low supply voltage available in handheld cheap devices. An exact mathematical model for the interpretation of FCC Regulations is derived. The radio coverage of UWB networking devices is determined and a chaos-based approach for the coverage extens...

The homotopy analysis method is used to find a family of solitary smooth hump solutions of the Camassa–Holm equation. This approximate solution, which is obtained as a series of exponentials, agrees well with the known exact solution. This paper complements the work of Wu & Liao [Wu W, Liao S. Solving solitary waves with discontinuity by means of the homotopy analysis method. Chaos, Solitons & ...

Using a variant of the interpolating Hamiltonian technique, we show that there exists, in the Sherrington-Kirkpatrick spin glass, an exact connection between the sample-to-sample fluctuations of the free energy and bond chaos involving 2and 4-replica overlaps between replicas with different but correlated bonds. This relation is used to derive an upper bound of the fluctuations. PACS numbers: 7...

We develop a theory describing the transition to a spatially homogeneous regime in a mixing flow with a chaotic in time reaction. The transverse Lyapunov exponent governing the stability of the homogeneous state can be represented as a combination of Lyapunov exponents for spatial mixing and temporal chaos. This representation, being exact for time-independent flows and equal Pe clet numbers of...

In this paper, based on a combination of homogenous balance and the rational expansion method, the exact analytical and closed-form solutions of the Duffing equation with cubic and quintic nonlinearities are derived. We focus on heteroclinic and homoclinic solutions which are relevant for the prediction of chaos in forced mechanical systems. The conditions of existence of these solutions which ...

We extend the theory of quasipotentials in dynamical systems by calculating an exact potential for the critical fluctuations of pitchfork bifurcations of period-doubling maps in the weak noise limit. These far-from-equilibrium fluctuations are described by finite-size mean field theory, placing their static properties in the same universality class as the Ising model on a complete graph. We dem...

In this article, we study the hyperbolic components of McMullen maps. We show that the boundaries of all hyperbolic components are Jordan curves. This settles a problem posed by Devaney. As a consequence, we show that cusps are dense on the boundary of the unbounded hyperbolic component. This is a dynamical analogue of McMullen’s theorem that cusps are dense on the Bers’ boundary of Teichmüller...