Hierarchy and stability of partially synchronous oscillations of diffusively coupled dynamical systems

The paper presents a qualitative analysis of an array of diffusively coupled identical continuous time dynamical systems.The effects of full, partial, anti-phase and in-phase-anti-phase chaotic synchronization are investigated via the linear invariant manifolds of the corresponding differential equations. Existence of various invariant manifolds, a self-similar behavior, a hierarchy and embedding of the manifolds of the coupled system are discovered. Sufficient conditions for the stability of the invariant manifolds are obtained via the method of Lyapunov functions. Conditions under which full global synchronization can not be achieved even for the largest coupling constant are defined. The general rigorous results are illustrated through examples of coupled Lorenz-like and coupled Rössler systems

Cluster synchronization in three-dimensional lattices of diffusively coupled oscillators

Cluster synchronization modes of continuous time oscillators that are diffusively coupled in a three-dimensional (3-D) lattice are studied in the paper via the corresponding linear invariant manifolds. Depending in an essential way on the number of oscillators composing the lattice in three volume directions, the set of possible regimes of spatiotemporal synchronization is examined. Sufficient conditions of the stability of cluster synchronization are obtained analytically for a wide class of coupled dynamical systems with complicated individual behavior. Dependence of the necessary coupling strengths for the onset of global synchronization on the number of oscillators in each lattice direction is discussed and an approximative formula is proposed. The appearance and order of stabilization of the cluster synchronization modes with increasing coupling between the oscillators are revealed for 2-D and 3-D lattices of coupled Lur'e systems and of coupled Rossler oscillators

Активні будинки, що виробляють енергію

This article outlines the problems of energy consumption and their solutions using technologies used in the construction of active houses with a positive energy balance. It reveals the concept of buildings that are combined with nature, which suggests that at home, being in balance with the outside world, should be as environmentally friendly and economical. The alternative energy sources are given, the most effective in the construction of such houses.В даній статті викладені проблеми енергоспоживання та їх вирішення за допомогою технологій, що застосовуються при будівництві активних будинків з позитивним енергобалансом. Розкривається концепція будівель, що поєднуються з природою, яка свідчить про те, що будинки, перебуваючи в балансі з навколишнім світом, повинні бути максимально екологічними і ощадливими. Наведено альтернативні джерела енергії, що найбільш ефективні при будівництві таких будинків

Cyclops states in repulsive Kuramoto networks: the role of higher-order coupling

Repulsive oscillator networks can exhibit multiple cooperative rhythms, including chimera and cluster splay states. Yet, understanding which rhythm prevails remains challenging. Here, we address this fundamental question in the context of Kuramoto-Sakaguchi networks of identical rotators with higher-order coupling. Through analysis and numerics, we show that three-cluster splay states with two distinct coherent clusters and a solitary oscillator are the prevalent rhythms in networks with an odd number of units. We denote such tripod patterns cyclops states with the solitary oscillator reminiscent of the Cyclops's eye. As their mythological counterparts, the cyclops states are giants that dominate the system's phase space in weakly repulsive networks with first-order coupling. Astonishingly, the addition of the second or third harmonics to the Kuramoto coupling function makes the cyclops states global attractors practically across the full range of coupling's repulsion. At a more general level, our results suggest clues for finding dominant rhythms in repulsive physical and biological networks

Morphometric study of hippocampal neurons in chronic immobilization stress

Hippocampus ensures the implementation of the memory mechanisms, behavioral reactions, including avoidance of stress, aversive effects etc. The study was performed on the material of 20 male Wistar rats weighing 220-250 g, 10 of which were intact control group and 10 were experimental group, in which chronic immobilization stress was simulated. We determined the relative number of neurons in multiple fields of view on the total area of the pyramidal and polymorphic layers of CA1 and CA3 regions (further recalculated per 10,000 μm), larger and smaller diameters of neuron’s bodies, their perimeters and areas with diameters of nuclei and nucleoli, nuclear-cytoplasmic rati

Breathing and switching cyclops states in Kuramoto networks with higher-mode coupling

Cyclops states are intriguing cluster patterns observed in oscillator networks, including neuronal ensembles. The concept of cyclops states formed by two distinct, coherent clusters and a solitary oscillator was introduced in [Munyayev {\it et al.}, Phys. Rev. Lett. 130, 107021 (2023)], where we explored the surprising prevalence of such states in repulsive Kuramoto networks of rotators with higher-mode harmonics in the coupling. This paper extends our analysis to understand the mechanisms responsible for destroying the cyclops' states and inducing new dynamical patterns called breathing and switching cyclops' states. We first analytically study the existence and stability of cyclops states in the Kuramoto-Sakaguchi networks of two-dimensional oscillators with inertia as a function of the second coupling harmonic. We then describe two bifurcation scenarios that give birth to breathing and switching cyclops states. We demonstrate that these states and their hybrids are prevalent across a wide coupling range and are robust against a relatively large intrinsic frequency detuning. Beyond the Kuramoto networks, breathing and switching cyclops states promise to strongly manifest in other physical and biological networks, including coupled theta-neurons

Sulfur content in needles of cedar (Pinus sibirica Du Tour) and siberian fir (Abies sibirica Ledeb.) of the Southern Baikal Region: Influence of industrial emissions

The paper presents the results of studying the sulfur content in the needles of cedar and Siberian fir of the Southern Baikal Region, carried out in the 2014–2015 period. The research aims to determine whether Baikal Pulp and Paper Mill (BPPM) are the primary stress factor of abiotic nature, which leads to the degradation of cedar and Siberian fir stands in the Southern Baikal Region. The authors have determined that the primary factor is the long-term impact of the emission of pollutants from heat power companies in the Irkutsk Region, as indicated by numerous studies using mathematical modeling methods. The research demonstrates that the assimilation organs of the cedar are more sensitive to the effects of sulfur dioxide compared to the needles of Siberian fir. Therefore, cedar needles can be considered as a more sensitive indicator of atmospheric pollution with sulfur dioxide. The authors have established that the primary source of contamination of Siberian fir needles is the SO₂ emission from the heat and power enterprises of the Irkutsk Region and not the emission of sulfur-containing compounds of the BPPM. The authors found that in the period from 2010 to 2019, the total SO₂ emissions from large industrial companies were an order of magnitude lower than the volumes of SO₂ emissions from heat power companies in the Irkutsk Region. These emissions will provoke a further deterioration in the state of the boreal forests of the Southern Baikal Region