اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدIncomplete noise-induced synchronization of spatially extended systems
76
0
0.0
(
0
)
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
A new type of noise-induced synchronous behavior is described. This phenomenon, called incomplete noise-induced synchronization, arises for one-dimensional Ginzburg-Landau equations driven by common noise. The mechanisms resulting in the incomplete noise-induced synchronization in the spatially extended systems are revealed analytically. The different model noise are considered. A very good agreement between the theoretical results and the numerically calculated data is shown.
قيم البحث
اقرأ أيضاً
Parameter estimation for spatiotemporal dynamics for coupled map lattices and continuous time domain systems is shown using a combination of multiple shooting, Karhunen-Loeve decomposition and Galerkins projection methodologies. The resulting advanta
ges in estimating parameters have been studied and discussed for chaotic and turbulent dynamics using small amounts of data from subsystems, availability of only scalar and noisy time series data, effects of space-time parameter variations, and in the presence of multiple time-scales.
Many systems may switch to an undesired state due to internal failures or external perturbations, of which critical transitions toward degraded ecosystem states are a prominent example. Resilience restoration focuses on the ability of spatially-exten
ded systems and the required time to recover to their desired states under stochastic environmental conditions. While mean-field approaches may guide recovery strategies by indicating the conditions needed to destabilize undesired states, these approaches are not accurately capturing the transition process toward the desired state of spatially-extended systems in stochastic environments. The difficulty is rooted in the lack of mathematical tools to analyze systems with high dimensionality, nonlinearity, and stochastic effects. We bridge this gap by developing new mathematical tools that employ nucleation theory in spatially-embedded systems to advance resilience restoration. We examine our approach on systems following mutualistic dynamics and diffusion models, finding that systems may exhibit single-cluster or multi-cluster phases depending on their sizes and noise strengths, and also construct a new scaling law governing the restoration time for arbitrary system size and noise strength in two-dimensional systems. This approach is not limited to ecosystems and has applications in various dynamical systems, from biology to infrastructural systems.
Many biological and chemical systems could be modeled by a population of oscillators coupled indirectly via a dynamical environment. Essentially, the environment by which the individual elements communicate is heterogeneous. Nevertheless, most of pre
vious works considered the homogeneous case only. Here, we investigated the dynamical behaviors in a population of spatially distributed chaotic oscillators immersed in a heterogeneous environment. Various dynamical synchronization states such as oscillation death, phase synchronization, and complete synchronized oscillation as well as their transitions were found. More importantly, we uncovered a non-traditional quorum sensing transition: increasing the density would first lead to collective oscillation from oscillation quench, but further increasing the population density would lead to degeneration from complete synchronization to phase synchronization or even from phase synchronization to desynchronization. The underlying mechanism of this finding was attributed to the dual roles played by the population density. Further more, by treating the indirectly coupled systems effectively to the system with directly local coupling, we applied the master stability function approach to predict the occurrence of the complete synchronized oscillation, which were in agreement with the direct numerical simulations of the full system. The possible candidates of the experimental realization on our model was also discussed.
This paper deals with two types of synchronous behavior of chaotic oscillators -- generalized synchronization and noise--induced synchronization. It has been shown that both these types of synchronization are caused by similar mechanisms and should b
e considered as the same type of the chaotic oscillator behavior. The mechanisms resulting in the generalized synchronization are mostly similar to ones taking place in the case of the noise-induced synchronization with biased noise.
Spatially extended systems, such as channel or pipe flows, are often equivariant under continuous symmetry transformations, with each state of the flow having an infinite number of equivalent solutions obtained from it by a translation or a rotation.
This multitude of equivalent solutions tends to obscure the dynamics of turbulence. Here we describe the `first Fourier mode slice, a very simple, easy to implement reduction of SO(2) symmetry. While the method exhibits rapid variations in phase velocity whenever the magnitude of the first Fourier mode is nearly vanishing, these near singularities can be regularized by a time-scaling transformation. We show that after application of the method, hitherto unseen global structures, for example Kuramoto-Sivashinsky relative periodic orbits and unstable manifolds of travelling waves, are uncovered.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
