Related papers: A Dynamic-Order Fractional Dynamic System
We consider the nonlinear Duffing oscillator in presence of fractional damping which is characteristic in different physical situations. The system is studied with a smaller and larger damping parameter value, that we call the underdamped…
The theory of derivative of noninteger order goes back to Leibniz, Liouville and Riemann. Derivatives of fractional order have found many applications in recent studies in mechanics, physics, economics. In this paper we define the…
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
Piecewise-linear nonlinear systems appear in many engineering disciplines. Prediction of the dynamic behavior of such systems is of great importance from practical and theoretical viewpoint. In this paper, a data-driven model order…
The "theory of open sub-functorial dynamics" is a new theory that defines interacting generalized dynamical systems. The interactions between these dynamics produce new dynamics which, of course, can then enter into other interactions. A…
Dynamical behaviour of discrete dynamical systems has been investigated extensively in the past few decades. However, in several applications, long term memory plays an important role in the evolution of dynamical variables. The definition…
Complex networks have become the main paradigm for modelling the dynamics of interacting systems. However, networks are intrinsically limited to describing pairwise interactions, whereas real-world systems are often characterized by…
Using the fractional integration and differentiation on R we build the fractional jet fibre bundle on a differentiable manifold and we emphasize some important geometrical objects. Euler-Lagrange fractional equations are described. Some…
This study makes the first attempt to use the 2/3-order fractional Laplacian modeling of enhanced diffusing movements of random turbulent particle resulting from nonlinear inertial interactions. A combined effect of the inertial…
Thermodynamics of trajectories promises to make possible the thorough analysis of the dynamical properties of an open quantum system, a sought-after goal in modern physics. Unfortunately, calculation of the relevant quantities presents…
This article develops a new mathematical method for holistic analysis of nonlinear dynamic compartmental systems through the system decomposition theory. The method is based on the novel dynamic system and subsystem partitioning…
We study forced oscillations of a rod with a body attached to its free end so that the motion of a system is described by two sets of equations, one of integer and the other of the fractional order. To the constitutive equation we associate…
Dynamical System has been widely used for encoding trajectories from human demonstration, which has the inherent adaptability to dynamically changing environments and robustness to perturbations. In this paper we propose a framework to…
In this letter we are concerned with the possibility to approach the existence of solutions to a class of discontinuous dynamical systems of fractional order. In this purpose, the underlying initial value problem is transformed into a…
A series of stationary principles are developed for dynamical systems by formulating the concept of mixed convolved action, which is written in terms of mixed variables, using temporal convolutions and fractional derivatives. Dynamical…
Fractals -- objects with non-integer dimensions -- occur in manifold settings and length scales in nature, ranging from snowflakes and lightning strikes to natural coastlines. Much effort has been expended to generate fractals for use in…
We propose the use of partial dynamical symmetry (PDS) as a selection criterion for higher-order terms in situations when a prescribed symmetry is obeyed by some states and is strongly broken in others. The procedure is demonstrated in a…
We consider a class of models describing an ensemble of identical interacting agents subject to multiplicative noise. In the thermodynamic limit, these systems exhibit continuous and discontinuous phase transitions in a, generally,…
We study a driven system in which interaction between particles causes their directional, coupled movement. In that model system, two particles move alternatingly in time on two coupled chains. Without interaction, both particles diffuse…
We introduce time-ordered multibody interactions to describe complex systems manifesting temporal as well as multibody dependencies. First, we show how the dynamics of multivariate Markov chains can be decomposed in ensembles of…