Slow–Fast Behaviors and Their Mechanism in a Periodically Excited Dynamical System with Double Hopf Bifurcations

This paper focuses on the influence of two scales in the frequency domain on the behaviors of a typical dynamical system with a double Hopf bifurcation. By introducing an external periodic excitation to the normal form of the vector field with double Hopf bifurcation at the origin and taking the exciting frequency far less than the natural frequency, a theoretical model with two scales in the frequency domain is established. Regarding the whole exciting term as a slow-varying parameter leads to a generalized autonomous system, in which the equilibrium branches and their bifurcations with the variation of the slow-varying parameter can be derived. With the increase of the exciting amplitude, different types of bifurcations may be involved in the generalized autonomous system, resulting in several qualitatively different forms of bursting attractors, the mechanism of which is presented by overlapping the transformed phase portraits and the bifurcations of the equilibrium branches. It is found that the single mode 2D torus may evolve to the bursting attractors with mixed modes, in which the trajectory alternates between the single mode oscillations and the mixed mode oscillations. Furthermore, the transitions between the quiescent states and the spiking states may not occur exactly at the bifurcation points because of the slow passage effect, while Hopf bifurcations may cause different forms of repetitive spiking oscillations.

From Frontier to Border: The 1845 Health Code and the Structuring of Greece’s Quarantine System

How did health technologies influence border construction, identityformation and political developments in nineteenth-century Greece? The study focuses on the 1845 Health Code, which instituted a comprehensive system of coastal and inland lazarettos and health offices. It presents the development of the health border system prior to the enactment of the code and explains the timing of the enactment of that legislation.Compared to other important health legislation, the code had a long gestation as a result of the combined and often conflicting influences of five interrelated factors: commercial relations with the Ottoman Empire; the health preoccupations of Western European states; the significance of the plague; the cultural orientation of the Greek state towards “Western civilisation”; and the capacity of the Greek administration to exercise control over its territory. The code, a step towards the geographical and cultural reorientation of a former Ottoman province as a sovereign state, defines the slow passage from the empire’s frontiers to the state border system.

On the Genesis of the Great Anthropological Transition

Today, humanity has entered an endless series of crisis states of practically all vi­tal forms of activity, which the global elites are already calling the “new nor­malcy”, and, in our opinion, this is only the initial stage of the Great Anthropolo­gical Transition. We can observe its manifestations today in anthropological, historical, socio-cultural, economic, medico-biological crisis phenomena, which demonstrating various options for the transition between two states of norm-homeostasis (in exact natural science, the term “phase transition” is often used). According to I. Prigogine and G. Haken, the transition or transit of the processes of becoming from one homeostasis to another always contain the following three consecutive phases against the background of an infinitely slow passage of crit­ical characteristics-calls or basic control parameters. A – the phase of death-dis­sociation of the outgoing order, returning its degrees of freedom to a subordinate level; B – the phase of the developed chaos of uncertainty and complexity at the subordinate level, in which the possible structures of an alternative future order fluctuate (are born and die for a short time); C – the phase of the birth of a new order through the capture by the fastest fluctuation of access to the resource of the system and fixing the system. The article substantiates the universality of such a structure for the development of a crisis and the possibility of managing it at each stage on the example of understanding social processes in a pandemic

On Fast–Slow Consensus Networks with a Dynamic Weight

We study dynamic networks under an undirected consensus communication protocol and with one state-dependent weighted edge. We assume that the aforementioned dynamic edge can take values over the whole real numbers, and that its behaviour depends on the nodes it connects and on an extrinsic slow variable. We show that, under mild conditions on the weight, there exists a reduction such that the dynamics of the network are organized by a transcritical singularity. As such, we detail a slow passage through a transcritical singularity for a simple network, and we observe that an exchange between consensus and clustering of the nodes is possible. In contrast to the classical planar fast–slow transcritical singularity, the network structure of the system under consideration induces the presence of a maximal canard. Our main tool of analysis is the blow-up method. Thus, we also focus on tracking the effects of the blow-up transformation on the network’s structure. We show that on each blow-up chart one recovers a particular dynamic network related to the original one. We further indicate a numerical issue produced by the slow passage through the transcritical singularity.

Example Three: Temporal Patterns in Limpet Foraging

This chapter presents a third example application of state- and prediction-based theory (SPT), again involving a behavior originally modeled via dynamic state variable modeling (DSVM). This example also addresses animal foraging, this time a choice of foraging activity. In this case, physiology has more important and interesting effects on behavior: the model animal, like many herbivores, can consume food relatively rapidly but does not assimilate its energy until the food's rather slow passage through a long gut. This leads to uncoupling of foraging behavior and energy assimilation on short time scales. The example is based directly on the DSVM analysis by Santini et al. of foraging behavior in the limpet Cella grata, which feeds by scraping rocks in the intertidal zone.

The effect of geriatric status on the subjective speed of time in elderly

The changes in the subjective passage of time at a later age is polyetiological and polymorphism. In this regard, the aim of this study is to investigate the nature of the impact of changes in geriatric status on the subjective speed of time flow at a old age. The study involved three groups of respondents: 55— 60 years — 120 people (17 men and 103 women, of 56.6±1.8 years); 61—74 years — 120 people (13 men and 107 women, 66,7±3.9 years) and 75—90 years — 50 (11 men and 39 women of 79.4±3.5 years). Research methods were divided into diagnostic units, focused on comprehensive geriatric assessment of the health status, as well as evaluating the specificity of the subjective speed of time in daily activities, past and present, and different ages of respondents. It is shown that in contrast to the chronological, subjective assessment of the age allows to detail the range of changes in the subjective passage of time at a old age. Older people who evaluated their subjective age, there has been rapid over time. When assessing subjective age chronological age is identical to the observed uncertainty in the rating of the subjective speed of time flow. Those respondents who evaluated their subjective age over chronological age noted the slow passage of time. It is shown that the level of education, status, social resources (work and family status), changes in geriatric status (polymorbidity, cognitive functioning, symptoms of depression and subjective feelings of loneliness), a subjective age are the predictors that determine the subjective speed of time flow at a old age.