Our purpose in this article is to study the asymptotic behavior of undamped evolution equations with fading memory on time-dependent spaces. By means of the theory of processes on time-dependent spaces, asymptotic a priori estimate and the technique...
We report the time-evolution of Probability Density Functions (PDFs) in a toy model of self-organised shear flows, where the formation of shear flows is induced by a finite memory time of a stochastic forcing, manifested by the emergence of a bimodal...
In this paper, we consider the backward asymptotically autonomous dynamical behavior for fractional non-autonomous nonclassical diffusion equations driven by a Wong–Zakai approximations process in Hs(Rn) with s∈(0,1). We first prove the ex...
Flat-topped one-dimensional maps have been used in the control of chaos in one-dimensional dynamical systems. In these applications, this mechanism is known as simple limiter control. In this paper, we will consider the introduction of simple limiter...
Stochastic processes are ubiquitous in nature and laboratories, and play a major role across traditional disciplinary boundaries. These stochastic processes are described by different variables and are thus very system-specific. In order to elucidate...
This work focused on demonstrating the use of dynamic time warping (DTW) as a metric for the elementary effects computation in Morris-based global sensitivity analysis (GSA) of model parameters in multivariate dynamical systems. One of the challenges...
This study explores the novel dynamics of the (3+1)-dimensional generalized Korteweg–de Vries–Zakharov–Kuznetsov (KdV-ZK) equation. A Galilean transformation is employed to derive the associated system of equations. Perturbing this...
The simplest geometry of the domain, for which internal wave attractors were for the first time investigated both experimentally and numerically, has the shape of a trapezium with one vertical wall and one inclined lateral wall, characterized by two...
Spiral waves are an intriguing phenomenon that can be found in a variety of chemical and biological systems. We consider the fractional-order resistor–capacitor shunted Josephson junction chaotic oscillator to investigate the spiral wave patter...
The relation between the complexity of a time-switched dynamics and the complexity of its control sequence depends critically on the concept of a non-autonomous pullback attractor. For instance, the switched dynamics associated with scalar dissipativ...
Brain dynamics can exhibit narrow-band nonlinear oscillations and multistability. For a subset of disorders of consciousness and motor control, we hypothesized that some symptoms originate from the inability to spontaneously transition from one attra...
We consider systems of differential equations with polynomial and rational nonlinearities and with a dependence on a discrete parameter. Such systems arise in biological and ecological applications, where the discrete parameter can be interpreted as...
When chaotic systems are used in different practical applications, such as chaotic secure communication and chaotic pseudorandom sequence generators, a large number of chaotic systems are strongly required. However, for a lack of a systematic constru...
In this paper, we define fractal synchronization (FS) based on the idea of stochastic synchronization and propose a mathematical apparatus for estimating FS. One major advantage of our proposed approach is that fractal synchronization makes it possib...
The chaotic dynamics observed in mathematical models of cancer can correspond to the unpredictable tumor growth and treatment responses seen in clinical settings. Suppressing this chaos is a significant challenge in theoretical oncology. This paper i...
This paper investigates the chaotic behavior of a modified jerk circuit with Chua’s diode. The Chua’s diode considered here is a nonlinear resistor having a symmetric piecewise linear voltage-current characteristic. To describe the system...
The modeling and prediction of chaotic time series require proper reconstruction of the state space from the available data in order to successfully estimate invariant properties of the embedded attractor. Thus, one must choose appropriate time delay...
A lightweight image encryption algorithm is presented based on chaos induction via a 5-dimensional hyperjerk oscillator (5DHO) network. First, the dynamics of our 5DHO network is investigated and shown to exhibit up to five coexisting hidden attracto...
The model of two species competing for a resource proposed by R. May and A.P. Shapiro has not yet been fully explored. We study its dynamic modes. The model reveals complex dynamics: multistable in-phase and out-of-phase cycles, and their bifurcation...
In this paper, we first used a Modified Numerical Approximation Method (NAM) and then a fractional Laplace Decomposition Method (LDM) to find the solution to the symmetric Rössler attractor. The newly proposed NAM is obtained through a nuanced d...
This paper presents Rain-Cloud Condensation Optimizer (RCCO), a nature-inspired metaheuristic that maps cloud microphysics to population-based search. Candidate solutions (“droplets”) evolve under a dual-attractor dynamic toward both a gl...
Background/Objectives: Synaptic plasticity is fundamental to learning and memory, yet classical models such as Hebbian learning and spike-timing-dependent plasticity often overlook the distributed and wave-like nature of neural activity. We present a...
As is well known, magnetic fields in space are distributed very inhomogeneously. Sometimes, field distributions have forms of filaments with high magnetic field values. As many observations show, such a filamentation takes place in convective cells i...
In this article, we investigate the fractional soliton solutions as well as the chaotic analysis of the fourth-order nonlinear Ablowitz–Kaup–Newell–Segur wave equation. This model is considered an intriguing high-order nonlinear par...