## 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

We study asymptotic behavior of the Darcy-Boussinesq system at large Darcy-Prandtl number. We prove that the global attractors for this system converge to that of the infinite Darcy-Prandtl number model. We also show the convergence of statistical properties including invariant measures.

CPAA

We consider the Trojan Y Chromosome (TYC) model for eradication of invasive species in population dynamics.
We present global estimates for the TYC system in a spatial domain.
In this work we prove the existence of a global attractor for the system.
We derive uniform estimates to tackle the question of asymptotic compactness of the semi-group for the TYC model in $H^2(\Omega)$. This along with the existence of a bounded absorbing set, which we also derive, demonstrates the existence of a global attractor for the TYC model.
The present analysis reveals that extinction of an invasive species is always possible to achieve irrespective of geometric considerations of the domain. This result is valid for TYC systems in which advection is negligible.
This theoretical work lays the foundation for experimental studies of the application of the TYC eradication strategy in spatial ecology, since the outcome is in principle guaranteed.

MBE

Control entropy (CE) is a complexity analysis suitable for
dynamic, non-stationary conditions which allows the inference of the control effort of a dynamical system generating the signal [4]. These characteristics make CE a highly relevant time varying quantity relevant to the dynamic physiological responses associated with running. Using High Resolution Accelerometry (HRA) signals we evaluate here constraints of running gait, from two different groups of runners, highly trained collegiate and untrained runners.
To this end, we further develop the control entropy (CE) statistic to allow for group analysis to examine the non-linear
characteristics of movement patterns in highly trained runners with those of untrained runners, to gain insight regarding gaits that are optimal for running. Specifically, CE develops response time series of individuals descriptive of the control effort; a group analysis of these shapes developed here uses Karhunen Loeve Analysis (KL) modes of these time series which are compared between groups by application of a Hotelling $T^{2}$ test to these group response shapes. We find that differences in the shape of the CE response exist within groups, between axes for untrained runners (vertical vs anterior-posterior and mediolateral vs anterior-posterior) and trained runners (mediolateral vs anterior-posterior). Also shape differences exist between groups by axes (vertical vs mediolateral). Further, the CE, as a whole, was higher in each axis in trained vs untrained runners. These results indicate that the approach can provide unique insight regarding the differing constraints on running gait in highly trained and untrained runners when running under dynamic conditions. Further, the final point indicates trained runners are less constrained than untrained runners across all running speeds.

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