18,327 research outputs found
Permanence and almost periodic solution of a multispecies Lotka-Volterra mutualism system with time varying delays on time scales
In this paper, we consider the almost periodic dynamics of a multispecies
Lotka-Volterra mutualism system with time varying delays on time scales. By
establishing some dynamic inequalities on time scales, a permanence result for
the model is obtained. Furthermore, by means of the almost periodic functional
hull theory on time scales and Lyapunov functional, some criteria are obtained
for the existence, uniqueness and global attractivity of almost periodic
solutions of the model. Our results complement and extend some scientific work
in recent years. Finally, an example is given to illustrate the main results.Comment: 31page
Formal Synthesis of Control Strategies for Positive Monotone Systems
We design controllers from formal specifications for positive discrete-time
monotone systems that are subject to bounded disturbances. Such systems are
widely used to model the dynamics of transportation and biological networks.
The specifications are described using signal temporal logic (STL), which can
express a broad range of temporal properties. We formulate the problem as a
mixed-integer linear program (MILP) and show that under the assumptions made in
this paper, which are not restrictive for traffic applications, the existence
of open-loop control policies is sufficient and almost necessary to ensure the
satisfaction of STL formulas. We establish a relation between satisfaction of
STL formulas in infinite time and set-invariance theories and provide an
efficient method to compute robust control invariant sets in high dimensions.
We also develop a robust model predictive framework to plan controls optimally
while ensuring the satisfaction of the specification. Illustrative examples and
a traffic management case study are included.Comment: To appear in IEEE Transactions on Automatic Control (TAC) (2018), 16
pages, double colum
Multi-class oscillating systems of interacting neurons
We consider multi-class systems of interacting nonlinear Hawkes processes
modeling several large families of neurons and study their mean field limits.
As the total number of neurons goes to infinity we prove that the evolution
within each class can be described by a nonlinear limit differential equation
driven by a Poisson random measure, and state associated central limit
theorems. We study situations in which the limit system exhibits oscillatory
behavior, and relate the results to certain piecewise deterministic Markov
processes and their diffusion approximations.Comment: 6 figure
Monotone and near-monotone biochemical networks
Monotone subsystems have appealing properties as components of larger networks, since they exhibit robust dynamical stability and predictability of responses to perturbations. This suggests that natural biological systems may have evolved to be, if not monotone, at least close to monotone in the sense of being decomposable into a “small” number of monotone components, In addition, recent research has shown that much insight can be attained from decomposing networks into monotone subsystems and the analysis of the resulting interconnections using tools from control theory. This paper provides an expository introduction to monotone systems and their interconnections, describing the basic concepts and some of the main mathematical results in a largely informal fashion
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