Local and global analysis of endocrine regulation as a non-cyclic feedback system

To understand the sophisticated control mechanisms of the human's endocrine system is a challenging task that is a crucial step towards precise medical treatment of many dysfunctions and diseases. Although mathematical models describing the endocrine system as a whole are still elusive, recently some substantial progress has been made in...

A Guiding Vector-Field algorithm for path-following control of nonholonomic mobile robots

In this paper, we propose an algorithm for path-following control of the nonholonomic mobile robot based on the idea of the guiding vector field (GVF). The desired path may be an arbitrary smooth curve in its implicit form, that is, a level set of a predefined smooth function. Using this function and the robot's kinematic model, we design a...

Guiding vector field algorithm for a moving path following problem

This paper presents a guidance algorithm solving the problem of moving path following, that is, steering a mobile robot to a curvilinear path attached to a moving frame. The nonholonomic robot is described by the unicycle-type model under the influence of some constant exogenous disturbance. The desired path may be an arbitrary smooth curve...

An impulsive model of endocrine regulation with two negative feedback loops

Whereas obtaining a global model of the human endocrine system remains a challenging problem, visible progress has been demonstrated in modeling its subsystems (axes) that regulate production of specific hormones. The axes are typically described by Goodwin-like cyclic feedback systems. Unlike the classical Goodwin oscillator, obeying a...

Opinion evolution in time-varying social influence networks with prejudiced agents

Investigation of social influence dynamics requires mathematical models that are “simple” enough to admit rigorous analysis, and yet sufficiently “rich” to capture salient features of social groups. Thus, the mechanism of iterative opinion pooling from (DeGroot, 1974), which can explain the generation of consensus, was elaborated in (Friedkin...

Modulus consensus in discrete-time signed networks and properties of special recurrent inequalities

Recently the dynamics of signed networks, where the ties among the agents can be both positive (attractive) or negative (repulsive) have attracted substantial attention of the research community. Examples of such networks are models of opinion dynamics over signed graphs. It has been shown that under mild connectivity assumptions these...

Synchronization of pulse-coupled oscillators and clocks under minimal connectivity assumptions

Populations of flashing fireflies, claps of applauding audience, cells of cardiac and circadian pacemakers reach synchrony via event-triggered interactions, referred to as pulse couplings. Synchronization via pulse coupling is widely used in wireless sensor networks, providing clock synchronization with parsimonious packet exchanges. In spite...