This review paper describes di®erent lumped circuitry realizations of the chaotic dynamical systems having equilibrium degeneration into a plane object with topological dimension of the equilibrium structure equals one. This property has limited amount (but still increasing, especially recently) of third-order autonomous deterministic dynamical systems. Mathematical models are generalized into classes to design analog networks as universal as possible, capable of modeling the rich scale of associated dynamics including the so-called chaos. Reference state trajectories for the chaotic attractors are generated via numerical analysis. Since used active devices can be precisely approximated by using third-level frequency dependent model, it is believed that computer simulations are close enough to capture real behavior. These simulations are included to demonstrate the existence of chaotic motion.

In the work [Chua, 1992], a deep intuition of its author gave rise to the choice of singularities corresponding to Chua's circuit. Therefore, it is the only one probably exhibiting three saddle points named Chua's singularities in this paper. One of the singularities is a saddle in forward time (dt > 0) of integration, whereas the other two are saddles in backward time (dt < 0) of integration. In the following, the term Chua's Chaos denotes chaos related to Chua's singularities. These singularities are the source of all special surfaces that are the subject of this contribution. We named the surface to which all other surfaces are bound as the Double-Arm Stable Manifold (DASM). The beauty and multifunctionality of this surface represents the unfathomable Intelligence in the sense of [Tolle, 2003]. The presence of the DASM in the state space is a sufficient condition for the generation of Chua's chaos or corresponding periodic windows. Since Chua's singularities are not limited by circuit morphology or the order of state equations, the research on Chua's chaos seems to be still very promising.

The paper compares the boundary surfaces using cross-sections in three projection planes, for the four changes of Chua's circuit parameters. It is known that due to changing the parameters, the Chua's circuit can be characterized not only by stable limit cycle, but also by one double scroll chaotic attractor, two single scroll chaotic attractors or other two stable limit cycles. Chua's circuit can even start working as a binary memory. It is not known yet, how changes in parameters, and consequently in attractors in the circuit, will affect the morphology of the boundary surface. The boundary surface separates the double scroll chaotic attractor from the stable limit cycle. In a variation of the parameters presented in this paper, the boundary surface will separate even single scroll chaotic attractors from each other. Dividing the state space into regions of attraction for different attractors, however, remains fundamentally the same.

In the article, we point out the need to measure the mass concentration of particulate matter (PM) in central Europe in a place of residence (a city and a small town), as PM has a negative impact on human health, especially that of children and the elderly. Since different amounts of PM (mainly peaks) were measured at two locations at a distance of 35 m from each other, a control measurement was also performed to verify the conformity of the measurements of both sensors, which was confirmed with measured courses of quantities. Cases of strong correlation (very close relationship) between PM10 and meteorological factors (temperature, humidity, barometric pressure) were found, but cases of no correlation were found as well, probably due to the effect of wind, which has not been measured yet. The article also points to the fact that, especially during the autumn/winter/spring heating season, the air quality in a small village may be worse than in a large city. This was also confirmed by the detected AQI sub-indices from PM2.5 and PM10. Due to the current rise in prices of gas and electricity, the use of wood combustion as a heating source is nowadays becoming increasingly more attractive, which may contribute to the worsening of the air quality in the future.

The paper deals with the measurement of individual size components of particulate matter focusing on typical particle size, mass, and number concentrations primarily in the city of Košice (Slovak republic) and the surrounding countryside. The deployment of the sensor IPS-7100 in the 2nd half of December 2022 allowed us to measure the particles smaller than the detection limit of other low-cost optical sensors—namely SPS30 and SEN54. The results show that although the mass concentration of ultrafine particles is negligible in comparison to fine and coarse particles, in terms of number concentration ultrafine particles make up the dominant component of particulate matter, which stands as a warning from the health point of view.

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The paper presents analyses of the implementation of IoT in the patent technology of the remote measuring laboratory (VMLab). The technology allows to create a new electrical connection between different devices, where the connection diagram was not defined before. This may be done remotely around the world. To begin with, an application of this technology as a remote measuring laboratory is presented and described. Analyses of the possible application of IoT technology in the Remote Measurement Laboratory (VMLAB) with a final design are also presented. The research focuses on an efficient way to retrieve measured values synchronized over the Internet from multiple measuring devices and controllable devices, without an Ethernet or Wi-Fi interface from the manufacturer. The analyses may also be useful when implementing an additional IoT approach to existing systems.

This paper briefly describes possibility to use band-pass and notch filters with low quality factors for straightforward synthesis of the so-called constant phase elements. These filters connected in cascade can form desired alternation of transfer function zeroes and poles. Using proposed approach one-quarter, half and threequarter fractional-order integrator dedicated for audio and speech applications has been derived and verified by using numerical analysis. Discovered method can be generalized to arbitrary frequency range, allowed phase error and almost any biquad topology.