TY - JOUR
T1 - Exponential Stability of Positive Conformable BAM Neural Networks with Communication Delays
AU - Dzung , Le Thi Hong
AU - Hien , Le Van
JO - Journal of Nonlinear Modeling and Analysis
VL - 2
SP - 453
EP - 475
PY - 2024
DA - 2024/06
SN - 6
DO - http://doi.org/10.12150/jnma.2024.453
UR - https://global-sci.org/intro/article_detail/jnma/23185.html
KW - Conformable derivative, time-delay systems, BAM neural networks, positive equilibrium, M-matrix.
AB - <p style="text-align: justify;">In this paper, we consider a class of nonlinear differential equations with delays described by conformable fractional derivative. This type
of differential equations can be used to describe dynamics of various practical models including biological and artificial neural networks with heterogeneous time-varying delays. By novel comparison techniques via fractional
differential and integral inequalities, we prove under assumptions involving
the order-preserving property of nonlinear vector fields that, with nonnegative
initial states and inputs, the system state trajectories are always nonnegative for all time. This feature, called positivity, induces a special character,
namely the monotonicity of the system. We then derive tractable conditions
in terms of linear programming and prove, by utilizing the Brouwer’s fixed
point theorem and comparisons induced by the monotonicity, that the system
possesses a unique positive equilibrium point which attracts exponentially all
state trajectories. An application to the exponential stability of fractional linear time-delay systems is also discussed. Numerical examples with simulations
are given to illustrate the theoretical results.</p>