Related papers: On the Melnikov method for fractional-order system…
Classical chaotic systems with symbolic dynamics but strong pruning present a particular challenge for the application of semiclassical quantization methods. In the present study we show that the technique of periodic orbit quantization by…
This chapter presents some numerical methods to solve problems in the fractional calculus of variations and fractional optimal control. Although there are plenty of methods available in the literature, we concentrate mainly on approximating…
Fractional calculus has been used to describe physical systems with complexity. Here, we show that a fractional calculus approach can restore or include complexity in any physical systems that can be described by partial differential…
A new method that enables easy and convenient discretization of partial differential equations with derivatives of arbitrary real order (so-called fractional derivatives) and delays is presented and illustrated on numerical solution of…
We consider time-periodic perturbations of analytically integrable systems in the sense of Bogoyavlenskij and study their \emph{real-meromorphic} nonintegrability, using a generalized version due to Ayoul and Zung of the Morales-Ramis…
According to the long-memory principle appears in fractional-order dynamical systems, analysis of these systems is commonly more complicated than those described by nonlinear ordinary differential equations. Another difficulty is due to the…
This study investigates the use of fractional order differential models to simulate the dynamic response of non-homogeneous discrete systems and to achieve efficient and accurate model order reduction. The traditional integer order approach…
In this paper, the solution of the multi-order differential equations, by using Mellin Transform, is proposed. It is shown that the problem related to the shift of the real part of the argument of the transformed function, arising when the…
Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent results show how bifurcations near resonances can be…
Numerical continuation techniques are powerful tools that have been extensively used to identify particular solutions of nonlinear dynamical systems and enable trajectory design in chaotic astrodynamics problems such as the Circular…
In this paper the chaos persistence in a class of discontinuous dynamical systems of fractional-order is analyzed. To that end, the Initial Value Problem is first transformed, by using the Filippov regularization [1], into a set-valued…
We are witnessing the birth of a new variety of pharmacokinetics where non-integer-order differential equations are employed to study the time course of drugs in the body: this is dubbed "fractional pharmacokinetics." The presence of…
In this paper, we study limit cycle bifurcations for a kind of non-smooth polynomial differential systems by perturbing a piecewise linear Hamiltonian system with a center at the origin and a homoclinic loop around the origin. By using the…
We show the existence of Shilnikov-type dynamics and bifurcation behaviour in general discrete three-dimensional piecewise smooth maps and give analytical results for the occurence of such dynamical behaviour. Our main example in fact shows…
The three-disk system, which for many years has served as a paradigm for the usefulness of cycle expansion methods, represents an extremely hard problem to semiclassical quantization when the disks are moved closer and closer together,…
We present a diffusion mechanism for time-dependent perturbations of autonomous Hamiltonian systems introduced in [25]. This mechanism is based on shadowing of pseudo-orbits generated by two dynamics: an `outer dynamics', given by…
A class of n-dimensional Poisson systems reducible to an unperturbed harmonic oscillator shall be considered. In such case, perturbations leaving invariant a given symplectic leaf shall be investigated. Our purpose will be to analyze the…
The resonant dynamics of a charged particle, governed by the Lorentz force equation in an electromagnetic field generated by a current-carrying wire with a small harmonic modulation, is considered in this study. When regarded as a…
The purpose of this paper is to develop a new effective approach to higher-order mixing in the semisimple setting. We prove effective exponential mixing of all orders for partially hyperbolic algebraic actions, under a strong spectral-gap…
Modeling of phenomena such as anomalous transport via fractional-order differential equations has been established as an effective alternative to partial differential equations, due to the inherent ability to describe large-scale behavior…