Related papers: Rijke tube: A nonlinear oscillator
We describe a possible general and simple paradigm in a classical thermal setting for discrete time crystals (DTCs), systems with stable dynamics which is subharmonic to the driving frequency thus breaking discrete time-translational…
Frequency domain analysis of linear time-invariant (LTI) systems in feedback with static nonlinearities is a classical and fruitful topic of nonlinear systems theory. We generalize this approach beyond equilibrium stability analysis with…
We propose lacunarity as a novel recurrence quantification measure and illustrate its efficacy to detect dynamical regime transitions which are exhibited by many complex real-world systems. We carry out a recurrence plot based analysis for…
Using experimental data from three different rogue wave supporting systems, determinism and predictability of the underlying dynamics are evaluated with methods of nonlinear time series analysis. We included original records from the…
Intractable phase dynamics often challenge our understanding of complex oscillatory systems, hindering the exploration of synchronisation, chaos, and emergent phenomena across diverse fields. We introduce a novel conceptual framework for…
Nonlinear topological insulators have garnered substantial recent attention as they have both enabled the discovery of new physics due to interparticle interactions, and may have applications in photonic devices such as topological lasers…
For the study of highly nonlinear, conservative dynamic systems, finding special periodic solutions which can be seen as generalization of the well-known normal modes of linear systems is very attractive. However, the study of…
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,…
Hybrid dynamical systems characterized by discrete switching of smooth dynamics have been used to model various rhythmic phenomena. However, the phase reduction theory, a fundamental framework for analyzing the synchronization of…
Complex dynamical systems-such as climate, ecosystems, and economics-can undergo catastrophic and potentially irreversible regime changes, often triggered by environmental parameter drift and stochastic disturbances. These critical…
We study scattering of a periodic wave in a string on two lumped oscillators attached to it. The equations can be represented as a driven (by the incident wave) dissipative (due to radiation losses) system of delay differential equations of…
The Turing instability is a paradigmatic route to patterns formation in reaction-diffusion systems. Following a diffusion-driven instability, homogeneous fixed points can become unstable when subject to external perturbation. As a…
We study the relationship between dynamical properties and interaction patterns in complex oscillator networks in the presence of noise. A striking finding is that noise leads to a general, one-to-one correspondence between the dynamical…
In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the…
A system of coupled oscillators on an arbitrary graph is locally driven by the tendency to mutual synchronization between nearby oscillators, but can and often exhibit nonlinear behavior on the whole graph. Understanding such nonlinear…
From optics to hydrodynamics, shock and rogue waves are widespread. Although they appear as distinct phenomena, new theories state that transitions between extreme waves are allowed. However, these have never been experimentally observed…
Nonlinear elastic effects play an important role in the dynamics of microelectromechanical systems (MEMS). Duffing oscillator is widely used as an archetypical model of mechanical resonators with nonlinear elastic behavior. In contrast,…
Dynamical systems theory describes how interacting quantities change over time and space, from molecular oscillators to large-scale biological patterns. Such systems often involve nonlinear feedbacks, delays, and interactions across scales.…
Nonlinear systems play a significant role in numerous scientific and engineering disciplines, and comprehending their behavior is crucial for the development of effective control and prediction strategies. This paper introduces a novel…
Complex systems are commonly modeled using nonlinear dynamical systems. These models are often high-dimensional and chaotic. An important goal in studying physical systems through the lens of mathematical models is to determine when the…