Related papers: Equilibrium Properties of Rate Control Protocols
Acyclic preferences recently appeared as an elegant way to model many distributed systems. An acyclic instance admits a unique stable configuration, which can reveal the performance of the system. In this paper, we give the statistical…
A nonlinear electronic circuit comprising of three nodes with a feedback loop is analyzed. The system has two stable states, a uniform state and a sinusoidal oscillating state, and it transitions from one to another by means of a Hopf…
This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…
This work considers load-balance control among the relays under the secure transmission protocol via relay cooperation in two-hop wireless networks without the information of both eavesdropper channels and locations. The available two-hop…
The fluid model has proven to be one of the most effective tools for the analysis of stochastic queueing networks, specifically for the analysis of stability. It is known that stability of a fluid model implies positive (Harris) recurrence…
Nonsmooth formulations of physical models are common, particularly in climate modeling. However, in many of these models, there is little justification for this modeling choice, and no mathematical indication that the resulting behavior in…
The dynamic response of power grids to small events or persistent stochastic disturbances influences their stable operation. Low-frequency inter-area oscillations are of particular concern due to insufficient damping. This paper studies the…
We discuss a bifurcation scenario which creates periodic pulsating solutions in slow-fast delayed systems through a cascade of almost simultaneous Hopf bifurcations. This scenario has been previously associated with formation of pulses in a…
Algorithms of control of differential equations solutions are under investigation in the article. Idealized and real modifications of the algorithms are distinguished. An equation, which can be the base equation for investigation of the…
Recently, a framework for controller design of sampled-data nonlinear systems via their approximate discrete-time models has been proposed in the literature. In this paper we develop novel tools that can be used within this framework and…
In this paper we analyze a simple mathematical model which describes the interaction between the proteins p53 and Mdm2. For the stationary state we discuss the local stability and the existence of the Hopf bifurcation. Choosing the delay as…
Filtered Smith predictors are well established for controlling linear plants with constant time delays. Apart from this classical application scenario, they are also employed within networked control loops, where the measurements are sent…
We study scalar delay equations $$\dot{x} (t) = \lambda f(x(t-1)) + b^{-1} (x(t) + x(t -p/2))$$ with odd nonlinearity $f$, real nonzero parameters $\lambda, \, b$, and two positive time delays $1,\ p/2$. We assume supercritical…
Gene regulatory networks, i.e. DNA segments in a cell which interact with each other indirectly through their RNA and protein products, lie at the heart of many important intracellular signal transduction processes. In this paper we analyse…
A cross-diffusion system modeling the information herding of individuals is analyzed in a bounded domain with no-flux boundary conditions. The variables are the species' density and an influence function which modifies the information state…
Reaction diffusion systems are often used to study pattern formation in biological systems. However, most methods for understanding their behavior are challenging and can rarely be applied to complex systems common in biological…
In this paper, we consider a bidirectional relay network with half-duplex nodes and block fading where the nodes transmit with a fixed transmission rate. Thereby, user 1 and user 2 exchange information only via a relay node, i.e., a direct…
Feedback control actively dissipates uncertainty from a dynamical system by means of actuation. We develop a notion of "control capacity" that gives a fundamental limit (in bits) on the rate at which a controller can dissipate the…
A class of hyperbolic reaction--diffusion models with cross-diffusion is derived within the context of Extended Thermodynamics. Linear stability analysis is performed to study the nature of the equilibrium states against uniform and…
A simple electronic circuit with a voltage controlled current source is investigated. The circuit exhibits rich dynamics upon varying the circuit elements such as L,C and R, and the control factor of the current source. Among several other…