Related papers: Fractional Dynamical Systems
Fractional systems with Riemann-Liouville derivatives are considered. The initial memory value problem is posed and studied. We obtain explicit steering laws with respect to the values of the fractional integrals of the state variables. The…
In this paper we will present some alternative types of mathematical description and methods of solution of the fractional-order dynamical system in the state space. We point out the difference in the true sense of the name "state" space…
In this paper, a nonlinear system of fractional ordinary differential equations with multiple scales in time is investigated. We are interested in the effective long-term computation of the solution. The main challenge is how to obtain the…
In this paper we discuss a concept of dynamic memory and an application of fractional calculus to describe the dynamic memory. The concept of memory is considered from the standpoint of economic models in the framework of continuous time…
In this article we address the problem of the nonlinear interaction of subdiffusive particles. We introduce the random walk model in which statistical characteristics of a random walker such as escape rate and jump distribution depend on…
Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically…
Recurrence networks are a novel tool of nonlinear time series analysis allowing the characterisation of higher-order geometric properties of complex dynamical systems based on recurrences in phase space, which are a fundamental concept in…
In this chapter we provide an introduction to fractional dissipative partial differential equations (PDEs) with a focus on trying to understand their dynamics. The class of PDEs we focus on are reaction-diffusion equations but we also…
In this paper we present stochastic foundations of fractional dynamics driven by fractional material derivative of distributed order-type. Before stating our main result we present the stochastic scenario which underlies the dynamics given…
Wave packet revivals and fractional revivals are hallmark quantum interference phenomena that arise in systems with nonlinear energy spectra, and their signatures in expectation values of observables have been studied extensively in earlier…
One unusual property of dynamic systems, whose state is characterized by a set of scalar dynamic variables satisfying a system of differential equations of a general form, is considered. This property is related to the behavior of equations…
It is shown that preferential concentrations of inertial (finite-size) particle suspensions in turbulent flows follow from the dissipative nature of their dynamics. In phase space, particle trajectories converge toward a dynamical fractal…
The stochastic scenario of relaxation in the complex systems is presented. It is based on a general probabilistic formalism of limit theorems. The nonexponential relaxation is shown to result from the asymptotic self-similar properties in…
Dynamical scaling is an asymptotic property typical for the dynamics of first-order phase transitions in physical systems and related to self-similarity. Based on the integral-representation for the marginal probabilities of a fractional…
In the paper we study the subject of positivity of systems with sequential fractional difference. We give formulas for the unique solutions of systems in linear and semi-linear cases. The positivity of systems is considered.
A classic approach in dynamical systems is to use particular geometric structures to deduce statistical properties, for example the existence of invariant measures with stochastic-like behaviour such as large deviations or decay of…
Discrete fractional order chaotic systems extends the memory capability to capture the discrete nature of physical systems. In this research, the memristive discrete fractional order chaotic system is introduced. The dynamics of the system…
Fractional-order dynamical systems are used to describe processes that exhibit long-term memory with power-law dependence. Notable examples include complex neurophysiological signals such as electroencephalogram (EEG) and blood-oxygen-level…
We investigate the geometric properties displayed by the magnetic patterns developing on a two-dimensional Ising system, when a diffusive thermal dynamics is adopted. Such a dynamics is generated by a random walker which diffuses throughout…
A criterion on the asymptotic stability of fractional-order systems with incomensurate orders is proposed in this paper. Existing methods always assume order parameters be rational numbers or the ratios of any two orders be rational…