## 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

In this paper, we study the transverse stability of random dynamical
systems (RDS). Suppose a RDS on a Riemann manifold possesses a
non-random invariant submanifold, what conditions can guarantee that
a random attractor of the RDS restrained on the invariant
submanifold is a random attractor with respect to the whole
manifold? By the linearization technique, we prove that if all the
normal Lyapunov exponents with respect to the tangent space of the
submanifold are negative, then the attractor on the submanifold is
also a random attractor of the whole manifold. This result extends
the idea of the transverse stability analysis of deterministic
dynamical systems in [1,3]. As an explicit example,
we discuss the complete synchronization in network of coupled maps
with both stochastic topologies and maps, which extends the
well-known master stability function (MSF) approach for
deterministic cases to stochastic cases.

JIMO

In this paper, the cluster synchronization for an array of linearly
coupled identical chaotic systems is investigated. New coupling
schemes (or coupling matrices) are proposed, by which global cluster
synchronization of linearly coupled chaotic systems can be realized.
Here, the number and the size of clusters (or groups) can be
arbitrary. Some sufficient criteria to ensure global cluster
synchronization are derived. Moreover, for any given coupling
matrix, new coupled complex networks with adaptive coupling
strengths are proposed, which can synchronize coupled chaotic
systems by clusters. Numerical simulations are finally given to show
the validity of the theoretical results.

NHM

We analyze stability of consensus algorithms in networks of
multi-agents with time-varying topologies and delays. The topology
and delays are modeled as induced by an adapted process and are rather
general, including i.i.d. topology processes, asynchronous consensus
algorithms, and Markovian jumping switching. In case the self-links are instantaneous, we prove that the network
reaches consensus for all bounded delays if the graph corresponding to the
conditional expectation of the coupling matrix sum across a finite
time interval has a spanning tree almost surely.
Moreover, when self-links are also delayed
and when the delays satisfy certain integer patterns, we
observe and prove that the algorithm may not reach consensus but
instead synchronize at a periodic trajectory, whose period depends
on the delay pattern. We also give a brief discussion on the
dynamics in the absence of self-links.

keywords:
Consensus
,
network of multi-agents
,
synchronization
,
adapted
process
,
switching topology.
,
delay

## Year of publication

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