COVID-19 PANDEMIC: DIRECTED OR NATURAL FLUCTUATION THAT CHANGES THE WORLD

The article presents a synergetic interpretation of the nature, mechanism, and role of the Covid-19 pandemic as a fluctuation that has undergone nucleation in the global system. The choice of methodological bases of our research is due to the fact that synergetics is considered today one of the new promising ways to understand the processes taking place in society, in social systems at the turning points of their development. We assume that this Covid-19 pandemic became the critical fluctuation that quickly spread throughout the world. Today, the global system is in a state of imbalance, in which old connections and structures have been destroyed or are being destroyed, and new ones have not yet been formed. As a result, it fell into the bifurcation zone, where further development becomes unpredictable. The modern world is facing another challenge of history. Therefore, today it is extremely important to determine the range of possible attractors of further evolution of the global system and, at the same time, those that are achievable and favorable to humanity. From a philosophical point of view, we can talk about being that appears before our eyes, about the birth of a new reality in which we have to live. It was found that the synergetic methodology involves the creation (consciously) of the necessary conditions for the introduction into the system of the desired fluctuation with signs of a new desired quality, and promote its nucleation. This will lead to the formation of new organizational integrity and the transition to a new evolutionary channel of development. That is why today, various conspiracy theories about the origin of the Covid-19 pandemic are actively spreading. The attitude to them is ambiguous. However, several facts force us to analyze them and draw appropriate conclusions carefully. It is noted that the lack of reliable information does not yet allow us to give an unambiguous answer about the nature of this fluctuation. However, there is no doubt that it has become a powerful factor in forming a new reality, a bifurcation transition to a new – and, so far, not clearly defined – attractor of the evolution of the global system.

Bifurcation transition in a system of two microwave oscillators during coherence destruction

The fine structure of bifurcation changes of oscillatory regimes in a system of two microwave oscillators in the region of mutual resonant strong coupling is experimentally investigated. Briefly discusses the methods for circuit implementation of strong resonant interactions, as well as their analytical threshold, above which synchronous modes lose stability and the system goes into dynamic chaos mode.

NONLINEAR PHENOMENA IN THE SINGLE-MODE DYNAMICS OF A CABLE-SUPPORTED BEAM

In this paper we discuss the practical usefulness of nonlinear dynamical analysis for the design of a planar cable-supported beam: we refer to a feasible case, assuming the value of the parameters corresponding to a realistic pedestrian footbridge. We consider a one degree of freedom model, obtained by the classical Galerkin reduction technique: the ensuing ordinary differential equation has both quadratic and cubic terms, due to geometric nonlinearities. Extensive numerical simulations are performed: they point out that this model, in spite of its apparent simplicity, is able to highlight the complex dynamics of the cable-supported beam, describing several common and uncommon nonlinear phenomena. Each of them is interpreted in terms of oscillations of the considered mechanical system; we explain the relevance of all the obtained results in the design of the examined structure under steady loads as wind and pedestrians, but also under transient phenomena as earthquake and gust; the ensuing issues, the most dangerous ranges and also the sensibility to perturbations are discussed in detail. In particular we deal with the importance, for an engineering design, of a careful interpretation of: isola bifurcation, transition to chaos both by period doubling cascade and reverse boundary crisis, multistability with coexistence of chaotic and periodic attractors, fractal basins boundaries, erosion of immediate basins, interrupted sequence of period doubling bifurcations. Also the effects of secondary attractors are analyzed, and it is shown that in general they cannot be neglected even if their range of existence is very small. We underline that all these investigations are performed choosing the excitation frequency far from resonances in order to alert the designer that the system dynamics may be complex independently of the activation mechanism due to resonance.

The Hide, Skeldon, Acheson dynamo revisited

Hide et al . (Hide, Skeldon & Acheson 1996 Proc. R. Soc. A 452 , 1369–1395) introduced a nonlinear system of three coupled ordinary differential equations to model a self-exciting Faraday disk homopolar dynamo. A very small selection of its possible behaviours was presented in that paper. Subsequent studies have extended the system to incorporate the effects of a nonlinear motor, an external battery and magnetic field, the coupling of two or more identical dynamos together, among other things. In this paper, we return to the original model with a view to perform a more extensive analysis of the Hide et al . dynamo. For the first time, we present bifurcation transition diagrams, so that the two examples of chaotic dynamo action (shown in figure 9 in that paper) can now be placed into context. We exhibit the coexistence of multiple attractors and also identify the lowest order unstable periodic orbits pertaining to some specific cases.

A Time-Dependent Bifurcation Model with Control and Pulsing Oscillations

A time-dependent bifurcation model and its control problem are studied. Firstly, the delayed bifurcating transition with memory effects due to time-dependent parameters are analysed. Secondly, a control problem with time-dependent parametric feedback in this bifurcation model is investigated. Finally, an important mechanism for pulsing oscillation is found as the result of the delayed bifurcation transition occurring when the bifurcation parameter varies periodically across the steady bifurcation value.

TIME-DEPENDENT BIFURCATION: A NEW METHOD AND APPLICATIONS

A new qualitative method is presented for studying the bifurcation problems of nonlinear systems with time-dependent parameters. The concept of stability on finite time intervals is introduced and some related stability theorems are established in order to analyze time-dependent bifurcation problems. As some applications of the new method, three different types of delayed bifurcation transitions and jump phenomena of time-dependent Duffing–van der Pol's equation are investigated qualitatively. The bifurcation transition values are predicted by constructing the V-functions or by the linear stability. The sensitivity of motion to the initial values and parameters is also discussed.

SELF-EXCITING FARADAY DISK HOMOPOLAR DYNAMOS

In this paper we present an overview of recently published work on the Faraday disk self-exciting homopolar dynamos. We also extend the analysis of two such coupled self-exciting disk dynamos with linear series motors [Moroz et al., 1998a; Moroz et al., 1998b] to the situation where one or both dynamo subunits incorporate nonlinear motors. We examine the differences in some of the bifurcation transition sequences between the various cases and consider whether the nonlinear quenching of oscillatory solutions can occur [Hide, 1998].