As space systems evolve towards cis-lunar missions and beyond, the demand for precise yet low-size, -weight, and -power (SWaP) clocks and synchronization methods becomes increasingly critical. We introduce a novel clock synchronization approach based...
The Kuramoto model is a classical model used for the describing of synchronization in populations of oscillatory units. In the present paper we study the Kuramoto model with delay with a focus on the distribution of the oscillators’ frequencies...
The Aharonov–Bohm effect can be described as a phase difference in interfering charged particles that travel through two distinct pathways oppositely surrounding a perpendicularly-positioned solenoid. The magnetic field emanates from the soleno...
In this paper, we consider the stochastic fractional-space Kuramoto–Sivashinsky equation forced by multiplicative noise. To obtain the exact solutions of the stochastic fractional-space Kuramoto–Sivashinsky equation, we apply the
The Kuramoto–Sinelshchikov–Velarde equation describes the evolution of a phase turbulence in reaction-diffusion systems or the evolution of the plane flame propagation, taking into account the combined influence of diffusion and thermal c...
In part I of this work to appear in Foudations-MDPI 2024, some existence and uniqueness results for the solutions of some equations were reviewed, such as the Korteweg–de Vries equation (KdV), the Kuramoto–Sivashinsky equation (KS), the g...
We present a synchronization transition study of the locally coupled Kuramoto model on extremely large graphs. We compare regular
In this article, we investigate the nonlinear model describing the various physical and chemical phenomena named the Kuramoto–Sivashinsky equation. We implemented the natural decomposition method, a novel technique, mixed with the Caputo–...
The generalized Kuramoto–Sivashinsky equation is investigated using the modified Kudryashov method for the new exact solutions. The modified Kudryashov method converts the given nonlinear partial differential equation to algebraic equations, as...
This paper investigates the stabilization for stochastic coupled Kuramoto oscillators (SCKOs) via nonlinear distributed feedback control. An original nonlinear distributed feedback control with the advantages of fast response, no steady-state deviati...
This work presents an efficient analytical framework based on the Natural Residual Power Series Method (NRPSM) for solving several forms of the time-fractional Kuramoto–Sivashinsky equation with the Caputo derivative. The proposed method avoids...
Timing skew is a critical bottleneck in high-speed Time-Interleaved (TI) Analog-to-Digital Converters (ADCs) that severely degrades dynamic range. This paper presents a mathematically rigorous, data-driven synchronization framework for calibrating ef...
This paper is intended to study noise-to-state stability in probability (NSSP) for random coupled Kuramoto oscillators with input control (RCKOIC). A feedback control is designed, which makes us give the existence and uniqueness of a solution for RCK...
This work investigates the complex dynamics of the stochastic fractional Kuramoto–Sivashinsky equation (SFKSE) with conformable fractional derivatives. The research begins with the creation of singular stochastic soliton solutions utilizing the...
In this paper, we present a collocation algorithm for numerically treating the time-fractional Kuramoto–Sivashinsky equation (TFKSE). Certain orthogonal polynomials, which are expressed as combinations of Chebyshev polynomials, and their shifte...
As the global energy structure transitions towards cleaner sources, large-scale integration of wind power has become a trend for modern power systems. However, the impact of low-inertia power electronic converters and the fault propagation effects at...
Soft-matter systems when driven out of equilibrium often give rise to structures that usually lie in between the macroscopic scale of the material and microscopic scale of its constituents. In this paper we review three such systems, the two-dimensio...
We study the realized power variations for the fourth order linearized Kuramoto–Sivashinsky (LKS) SPDEs and their gradient, driven by the space–time white noise in one-to-three dimensional spaces, in time, have infinite quadratic variatio...
The main objective of this paper is to introduce and study the numerical solutions of the multi-space fractal-fractional Kuramoto-Sivashinsky equation (MSFFKS) and the multi-space fractal-fractional Korteweg-de Vries equation (MSFFKDV). These models...
The primary purpose of this paper is to discuss whether NEV enterprises can achieve synchronous effects with the whole Chinese automobile industry in terms of growth mode. In this paper, we study the development of new energy vehicles from the perspe...
The synchronization of an ensemble of oscillators is a phenomenon present in systems of different fields, ranging from social to physical and biological systems. This phenomenon is often described mathematically by the Kuramoto model, which assumes o...
Because of its sensitivity to the instantaneous structure factor, S(Q,t = 0), Extended X-ray Absorption Fine Structure (EXAFS) is a powerful tool for probing the dynamic structure of condensed matter systems in which the charge and lattice dynamics a...
The Kuramoto–Sivashinsky (KS) equation and its fractional generalizations (FKSs) arise as canonical models for a wide class of nonlinear dissipative–dispersive systems, including thin-film flows, combustion fronts, drift–wave turbul...
The second-order Kuramoto equation describes the synchronization of coupled oscillators with inertia, which occur, for example, in power grids. On the contrary to the first-order Kuramoto equation, its synchronization transition behavior is significa...
Model-based reinforcement learning (MBRL) is a promising approach for achieving high sample efficiency in learning control policies. The existing world models in MBRL typically represent the environment’s state as a single global latent vector....
This paper reviews the results of existence and uniqueness of the solutions of these equations: the Korteweg–De Vries equation, the Kuramoto–Sivashinsky equation, the generalized Korteweg–De Vries–Kuramoto–Sivashinsky eq...
A new class of problems in free surface hydrodynamics appeared after the groundbreaking discovery by Yves Couder and Emmanuel Fort. A bouncing droplet in association with Faraday surface waves gives rise to new nonlinear dynamics, in analogy with the...
In the study of disordered hyperuniformity, which bridges ordered and disordered states and has broad implications in physics and biology, active matter systems offer a rich platform for spontaneous pattern formation. This work investigates frustrate...
Let
We investigate spatial moduli of non-differentiability for the fourth-order linearized Kuramoto–Sivashinsky (L-KS) SPDEs and their gradient, driven by the space-time white noise in one-to-three dimensional spaces. We use the underlying explicit kerne...
We establish the similarity in two model-based reconstructions of the coupling between the polar magnetic fields of the Sun represented by the solar faculae time series. The reconstructions are inferred from the pair of the coupled oscillators modell...
This work reveals an advanced numerical scheme for obtaining approximate solutions to nonlinear fractional Kuramoto–Sivashinsky (K-S) equations involving Caputo derivatives. We introduce the Sumudu transform (ST), which converts the fractional...
Transferring observed gait coordination into executable Central Pattern Generator (CPG) specifications remains challenging because networks are often tuned empirically without systematic links to measured biomechanics. This study presents a biomechan...
In this integrative review paper, we explore the parallels between the physical models of gyrotrons and some equations used in diverse and broad scientific fields. These include Adler’s famous equation, Van der Pol equation, the Lotka–Vol...
The concept of ranked order probability distribution unveils natural probabilistic interpretations for the kink waves (and hence the solitons) solving higher order dispersive Burgers’ type PDEs. Thanks to this underlying structure, it is possib...
This paper investigates the fixed-time synchronization problem of a Kuramoto–oscillator network in the presence of a pacemaker. Based on the framework of the cyber-physical system (CPS), fixed-time synchronization criteria of such network are p...
This work integrates the fast Alikhanov method with a compact scheme to solve the time-fractional Kuramoto–Sivashinsky (KS) equation with the generalized Burgers’ type nonlinearity. Initially, the Alikhanov algorithm, designed to handle t...
Particles moving in a fluid interact through the flow field they generate, which can lead to complex nonlinear dynamics. One important example is the synchronization of oscillatory motion in biological systems, such as the coordinated beating of cili...
Prolific growth of sensors and sensor technology has resulted various applications in sensing, monitoring, assessment and control operations. Owing to the large number of sensing units the the aggregate data volume creates a burden to the central dat...
Oscillatory neural networks (ONNs) provide a neuromorphic computing framework that exploits the phase dynamics of coupled oscillators for parallel and energy-efficient pattern recognition. In this study, we design a single-layer, fully connected ONN...
Central pattern generators (CPGs) have been extensively researched and validated as a well-established methodology for bionic control, particularly within the field of legged robotics. However, investigations concerning octopod robots remain relative...
Power-law distributed cascade failures are well known in power-grid systems. Understanding this phenomena has been done by various DC threshold models, self-tuned at their critical point. Here, we attempt to describe it using an AC threshold model, w...
Coordination is a ubiquitous feature of all living things. It occurs by virtue of informational coupling among component parts and processes and can be quite specific (as when cells in the brain resonate to signals in the environment) or nonspecific...
Full-body movement involving multi-segmental coordination has been essential to our evolution as a species, but its study has been focused mostly on the analysis of one-dimensional data. The field is poised for a change by the availability of high-de...
We study three multistep implicit–explicit (IMEX) time discretizations coupled with a local discontinuous Galerkin (LDG) spatial discretization for a class of one-dimensional nonlinear fourth-order partial differential equations (PDEs), with pa...
The Kuramoto–Sivashinsky (KS) equation and its fractional form (FKS) are widely used across scientific fields, including fluid dynamics, plasma physics, and chemical processes, to model nonlinear phenomena such as shock waves. It is worth empha...
Adaptive interactions are an important property of many real-word network systems. A feature of such networks is the change in their connectivity depending on the current states of the interacting elements. In this work, we study the question of how...
Synchronization in networks of conductance-based neurons depends on the external stimulus, coupling architecture, coupling strength, and initial state of the constituent cells. In this work, we numerically investigate a finite all-to-all network of i...
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Adaptive network models arise when describing processes in a wide range of fields and are characterized by some specific effects. One of them is mixed dynamics, which is the third type of chaos in addition to the conservative and dissipative types. I...
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