arXiv subjects

Marius-F. Danca

Publications and source records attributed to Marius-F. Danca.

40 records · Page 3Linked to original sources

arXiv2011

Synthesizing the Lü attractor by parameter-switching

In this letter we synthesize numerically the Lü attractor starting from the generalized Lorenz and Chen systems, by switching the control parameter inside a chosen finite set of values on every successive adjacent finite time intervals. A numerical method with fixed step size for ODEs is used to integrate the underlying initial value problem. As numerically and computationally proved in this work, the utilized attractors synthesis algorithm introduced by the present author before, allows to synthesize the Lü attractor starting from any finite set of parameter values.

nlin.CD↗

arXiv2011

A multistep algorithm for ODEs

The objective of this paper is to prove the convergence of a linear implicit multi-step numerical method for ordinary differential equations. The algorithm is obtained via Taylor approximations. The convergence is proved following the Dahlquist theory. As an additional topic, the time stability is established too. Comparative tests between some of the most known numerical methods and this method are presented.

nlin.CD↗

arXiv2011

Chaotic behavior of a class of discontinuous dynamical systems of fractional-order

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 problem of fractional-order, then by Cellina's approximate selection theorem [2, 3], the problem is approximated into a single-valued fractional-order problem, which is numerically solved by using a numerical scheme proposed by Diethelm, Ford and Freed [4]. Two typical examples of systems belonging to this class are analyzed and simulated.

nlin.CD↗

arXiv2011

Approach of a class of discontinuous dynamical systems of fractional order: existence of the solutions

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 fractional set-valued problem. Next, the Cellina's Theorem is applied leading to a single-valued continuous initial value problem of fractional order. The existence of solutions is assured by a Péano like theorem for ordinary differential equations of fractional order.

nlin.CD↗