Related papers: Stability Principle Underlying Passive Dynamic Wal…
We study stability properties of kinks for the (1+1)-dimensional nonlinear scalar field theory models \begin{equation*} \partial_t^2\phi -\partial_x^2\phi + W'(\phi) = 0, \quad (t,x)\in\mathbb{R}\times\mathbb{R}. \end{equation*} The orbital…
Many biological phenomena such as locomotion, circadian cycles, and breathing are rhythmic in nature and can be modeled as rhythmic dynamical systems. Dynamical systems modeling often involves neglecting certain characteristics of a…
Stability is a fundamental notion in dynamical systems and control theory that, traditionally understood, describes asymptotic behavior of solutions around an equilibrium point. This notion may be characterized abstractly as continuity of a…
This paper investigates the global stability and the global asymptotic stability independent of the sizes of the delays of linear time-varying Caputo fractional dynamic systems of real fractional order possessing internal point delays. The…
This paper provides a comprehensive analysis of stability and long-time behaviour of a coupled system constituted by two rigid bodies separated by a thin layer of lubricant. We show that permanent rotations of the whole system, with the…
We prove a strong law of large numbers and an annealed invariance principle for a random walk in a one-dimensional dynamic random environment evolving as the simple exclusion process with jump parameter $\gamma$. First, we establish that if…
The Random Walk Pinning Model (RWPM) is a statistical mechanics model in which the trajectory of a continuous time random walk $X=(X_t)_{t\geq 0}$ is rewarded according to the time it spends together with a moving catalyst. More…
This paper studies the problem of passive grasp stability under an external disturbance, that is, the ability of a grasp to resist a disturbance through passive responses at the contacts. To obtain physically consistent results, such a…
One of the most widely studied dynamical systems in nonlinear control theory is the levitated ball. Several full-state feedback controllers that ensure asymptotic regulation of the ball position have been reported in the literature.…
In this paper we explore the stabilization of closed invariant sets for passive systems, and present conditions under which a passivity-based feedback asymptotically stabilizes the goal set. Our results rely on novel reduction principles…
We use the entropy method to analyze the nonlinear dynamics and stability of a continuum kinetic model of an active nematic suspension. From the time evolution of the relative entropy -- an energy-like quantity in the kinetic model -- we…
Stability is a basic requirement when studying the behavior of dynamical systems. However, stabilizing dynamical systems via reinforcement learning is challenging because only little data can be collected over short time horizons before…
This work primarily focuses on an operator inference methodology aimed at constructing low-dimensional dynamical models based on a priori hypotheses about their structure, often informed by established physics or expert insights. Stability…
We prove an asymptotic stability result for the water wave equations linearized around small solitary waves. The equations we consider govern irrotational flow of a fluid with constant density bounded below by a rigid horizontal bottom and…
We consider an ensemble of mass collisionless particles, which interact mutually either by an attraction of Newton's law of gravitation or by an electrostatic repulsion of Coulomb's law, under a background downward gravity in a…
Now a standard in Nonlinear Sciences, the Kuramoto model is the perfect example of the transition to synchrony in heterogeneous systems of coupled oscillators. While its basic phenomenology has been sketched in early works, the…
In this paper we present a general tool to handle the presence of zero dynamics which are asymptotically but not locally exponentially stable in problems of robust nonlinear stabilization by output feedback. We show how it is possible to…
This paper introduces and studies the notion of output-input stability, which represents a variant of the minimum-phase property for general smooth nonlinear control systems. The definition of output-input stability does not rely on a…
Asymptotic safety is a set of conditions, based on the existence of a nontrivial fixed point for the renormalization group flow, which would make a quantum field theory consistent up to arbitrarily high energies. After introducing the basic…
The dynamics and stability of a fluid-filled hollow cylindrical shell rolling on an inclined plane are analyzed. We study the motion in two dimensions by analyzing the interaction between the fluid and the cylindrical shell. An analytical…