## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- AIMS Mathematics
- Conference Publications
- Electronic Research Announcements
- Mathematics in Engineering

### Open Access Journals

DCDS-B

In this paper, we construct an open and dense set in the space of bounded linear random dynamical systems (both discrete and continuous time) equipped with the essential sup norm such that the Lyapunov exponents depend analytically on the coefficients in this set. As a consequence, analyticity for Lyapunov exponents of bounded linear random dynamical systems is a generic property.

DCDS-B

In this paper, we give a criterion on instability of an equilibrium of a nonlinear Caputo fractional differential system. More precisely, we prove that if the spectrum of the linearization has at least one eigenvalue in the sector

$\left\{ \lambda \in \mathbb{C}\setminus \{0\}:|\arg (\lambda )| < \frac{\alpha \pi }{2} \right\},$ |

where

is the order of the fractional differential system, then the equilibrium of the nonlinear system is unstable.

$α∈ (0,1)$ |

DCDS-B

Nonautonomous differential equations on finite-time intervals play
an increasingly important role in applications that incorporate
time-varying vector fields, e.g. observed or forecasted velocity
fields in meteorology or oceanography which are known only for
times $t$ from a compact interval. While classical dynamical
systems methods often study the behaviour of solutions as $t \to
\pm\infty$, the dynamic partition (originally called the EPH
partition) aims at describing and classifying the finite-time
behaviour. We discuss fundamental properties of the dynamic
partition and show that it locally approximates the nonlinear
behaviour. We also provide an algorithm for practical computations
with dynamic partitions and apply it to a nonlinear 3-dimensional
example.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]