Related papers: Linear Response for Intermittent Circle Maps
This paper considers robust stability analysis of a large network of interconnected uncertain systems. To avoid analyzing the entire network as a single large, lumped system, we model the network interconnections with integral quadratic…
We apply the linear response theory developed in \cite{Ruelle} to analyze how a periodic signal of weak amplitude, superimposed upon a chaotic background, is transmitted in a network of non linearly interacting units. We numerically compute…
Recently, the stochastic asymptotical regularization (SAR) has been developed in (\emph{Inverse Problems}, 39: 015007, 2023) for the uncertainty quantification of the stable approximate solution of linear ill-posed inverse problems. In this…
A cone spherical metric is called irreducible if any developing map of the metric does not have monodromy in ${\rm U(1)}$. By using the theory of indigenous bundles, we construct on a compact Riemann surface $X$ of genus $g_X \geq 1$ a…
We consider families of multimodal interval maps with polynomial growth of the derivative along the critical orbits. For these maps Bruin and Todd have shown the existence and uniqueness of equilibrium states for the potential…
We show cocycle stability for linear maps with a weak irreducibility condition and their jointly integrable perturbations.
A rapid predictive tool based on the linearised Reynolds-averaged Navier-Stokes equations is proposed in this work to investigate secondary currents generated by streamwise-independent surface topography modulations in turbulent channel…
We identify a relationship between a random walk on a certain Euclidean lattice and incidence matrices of balanced incomplete block designs. We then compute the return probability of the random walk and use it to obtain the asymptotic…
The regularity of monotone transport maps plays an important role in several applications to PDE and geometry. Unfortunately, the classical statements on this subject are restricted to the case when the measures are compactly supported. In…
Direct numerical simulations are conducted to study the receptivity and transition mechanisms in a solitary wave boundary layer developing over randomly organized wave-like bottom topography. The boundary layer flow shows a selective…
The class of stochastic Runge-Kutta methods for stochastic differential equations due to R\"o{\ss}ler is considered. Coefficient families of diagonally drift-implicit stochastic Runge-Kutta (DDISRK) methods of weak order one and two are…
In this paper, we consider robust stability analysis of large-scale sparsely interconnected uncertain systems. By modeling the interconnections among the subsystems with integral quadratic constraints, we show that robust stability analysis…
The main contribution of this paper is a six-step semi-automatic algorithm that obtains a recursion satisfied by a family of determinants by systematically and iteratively applying Laplace expansion to the underlying matrix family. The…
Reaction-diffusion equations coupled to ordinary differential equations (ODEs) may exhibit spatially low-regular stationary solutions. This work provides a comprehensive theory of asymptotic stability of bounded, discontinuous or…
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…
Many complex engineering systems consist of multiple subsystems that are developed by different teams of engineers. To analyse, simulate and control such complex systems, accurate yet computationally efficient models are required. Modular…
We consider C^2 families t->f_t of C^4 nondegenerate unimodal maps. We study the absolutely continuous invariant probability (SRB) measure m_t of f_t, as a function of t on the set of Collet-Eckmann (CE) parameters: Upper bounds: Assuming…
Within the context of recursive least squares (RLS) parameter estimation, the goal of the present paper is to study the effect of regularization-induced bias on the transient and asymptotic accuracy of the parameter estimates. We consider…
A linear stability analysis of a single-phase Coupled Natural Circulation Loop (CNCL) is carried out using a Fourier series based 1-D model. A 3-D CFD study is undertaken to assess the ability of the 1-D model to capture the non-periodic…
We consider invertible discrete-time dynamical systems having a hyperbolic product structure in some region of the phase space with infinitely many branches and variable recurrence time. We show that the decay of correlations of the SRB…