In this report, a control method for the stabilization of periodic orbits for a class of one- and two-dimensional discrete-time systems that are topologically conjugate to symbolic dynamical systems is proposed and applied to a population model in an ecosystem and the Smale horseshoe map. A periodic orbit is assigned as a target by giving a sequence in which symbols have periodicity. As a consequence, it is shown that any periodic orbits can be globally stabilized by using arbitrarily small control inputs. This work is a new attempt to systematically design a control system based on symbolic dynamics in the sense that one estimates the magnitude of control inputs and analyzes the Lyapunov stability.
The altered regulation of autonomic response to mental stress can result in increased cardiovascular risk. The laboratory tests used to simulate the autonomic responses to real-life stressors do not necessarily induce generalized sympathetic activation; therefore, the assessment of regulatory outputs to different effector organs could be important. We aimed to study the cardiovascular sympathetic arousal in response to different mental stressors (Stroop test, mental arithmetic test) in 20 healthy students. The conceivable sympathetic vascular index - spectral power of low frequency band of systolic arterial pressure variability (LF-SAP) and novel potential cardiosympathetic index - symbolic dynamics heart rate variability index 0V% were evaluated. The heart and vessels responded differently to mental stress - while Stroop test induced increase of both 0V% and LF-SAP indices suggesting complex sympathetic arousal, mental arithmetic test evoked only 0V% increase compared to baseline (p<0.01, p<0.001, p<0.01, respectively). Significantly greater reactivity of LF-SAP, 0V%, heart rate (HR) and mean arterial pressure (MAP) were found in response to Stroop test compared to mental arithmetic test potentially indicating the effect of different central processing (0V%, LF-SAP: p<0.001; HR, MAP: p<0.01). The different effectors’ sympathetic responses to cognitive stressors could provide novel important information regarding potential pathomechanisms of stress-related diseases., M. Mestanik, A. Mestanikova, Z. Visnovcova, A. Calkovska, I. Tonhajzerova., and Obsahuje bibliografii
In the paper, a possible characterization of a chaotic behavior for the generalized semiflows in finite time is presented. As a main result, it is proven that under specific conditions there is at least one trajectory of generalized semiflow, which lies inside an arbitrary covering of the solution set. The trajectory mutually connects each subset of the covering. A connection with symbolic dynamical systems is mentioned and a possible numerical method of analysis of dynamical behavior is outlined.