Related papers: Fractional dynamics and recurrence analysis in can…
High-dimensional dynamical systems of interacting degrees of freedom are ubiquitous in the study of complex systems. When the directed interactions are totally uncorrelated, sufficiently strong and non-linear, many of these systems exhibit…
We provide appropriate tools for the analysis of dynamics and chaos for one-dimensional systems with periodic boundary conditions. Our approach allows for the investigation of the dependence of the largest Lyapunov exponent on various…
We investigate the Lyapunov spectrum of separated flows and their dependence on the numerical discretization. The chaotic flow around the NACA 0012 airfoil at low Reynolds number and large angle of attack is considered to that end, and t-,…
Based on the continuous time random walk, we derive the Fokker-Planck equations with Caputo-Fabrizio fractional derivative, which can effectively model a variety of physical phenomena, especially, the material heterogeneities and structures…
On the basis of a mathematical model, we continue the study of the metabolic Krebs cycle (or the tricarboxilic acid cycle). For the first time, we consider its consistency and stability, which depend on the dissipation of a transmembrane…
We discuss the alpha-muon sticking coefficient in the muon-catalysed ``in flight" d-t fusion in the framework of the Constrained Molecular Dynamics model. Especially the influence of muonic chaotic dynamics on the sticking coefficient is…
We analyzed conditions for Hopf and Turing instabilities to occur in two-component fractional reaction-diffusion systems. We showed that the eigenvalue spectrum and fractional derivative order mainly determine the type of instability and…
Dynamical fluctuations or rare events associated with atypical trajectories in chaotic maps due to specific initial conditions can crucially determine their fate, as the may lead to stability islands or regions in phase space otherwise…
Many physical, biological, and engineered systems exhibit memory effects that challenge Markovian models. Fractional calculus provides nonlocal operators to capture hereditary dynamics. This survey connects modeling, analysis, and…
Purpose: Chaotic diffusion in the non-linear systems is commonly studied in the action framework. In this paper, we show that the study in the frequency domain provides good estimates of the sizes of the chaotic regions in the phase space,…
This paper is concerned with analysis of coupled fractional reaction-diffusion equations. It provides analytical comparison for the fractional and regular reaction-diffusion systems. As an example, the reaction-diffusion model with cubic…
Cell-based models provide a helpful approach for simulating complex systems that exhibit adaptive, resilient qualities, such as cancer. Their focus on individual cell interactions makes them a particularly appropriate strategy to study the…
In this paper, a delay differential equations (DDEs) model of leukemia is introduced and its dynamical properties are investigated in comparison with the modified fractional-order system where the Caputo's derivative is used. The model…
Stochastic resetting is a rapidly developing topic in the field of stochastic processes and their applications. It denotes the occasional reset of a diffusing particle to its starting point and effects, inter alia, optimal first-passage…
High-dimensional chaotic dynamical systems can exhibit strongly transient features. These are often associated with instabilities that have finite-time duration. Because of the finite-time character of these transient events, their…
In the study of chaotic behaviour of systems of many hard spheres, Lyapunov exponents of small absolute value exhibit interesting characteristics leading to speculations about connections to non-equilibrium statistical mechanics. Analytical…
We study how dynamical quantities such as Lyapunov exponents, metric entropy, topological pressure, recurrence rates, and dimension-like characteristics change under a time reparameterization of a dynamical system. These quantities are…
This paper deals with hybrid systems (HS) with fractional order dynamics and their stability. The stability of two particular types of fractional order hybrid systems (FOHS), i.e., switching and reset control systems, is studied. Common…
Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires…
Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. In this work we introduce a new fractional operator…