Synchronized Attractors and Phase Entrained with Cavity Loss of the Coupled Laser’s Map

The laser differential equations are used to transform them into identical coupled maps. Valuable results are deduced during analytical and numerical studies on cavity loss. Phase and spatiotemporal synchronized attractors are observed via quasi-chaos under a certain range of controlling parameters, and symmetry breaking of chaotic attractors due to collision with their basin boundaries, and transpire differently from the previous attractors. During the numerical simulation, it is found that the sequence of repeated strange attractors if the coupling strength further increases, which are orthogonal mirror images (the dynamics of the system is the same at different values of controlling parameters). Moreover, it can help us to predict future problems and their solutions based on current issues, if we develop this model in more general.

Switching between Dissipative and Conservative Behaviors in a Modified Hyperchaotic System with the Variation of Its Parameter

The paper reports a modified 4D autonomous hyperchaotic system with an unusual characteristic. The modified system exhibits dissipative behavior for some ranges of a parameter and conservative behavior for the other ranges of the same parameter. Thus, there is a switching between dissipative and conservative behaviors of the proposed system. In the conservative range, the system exhibits chaotic orbit. Again in the dissipative range, the system, with its considered sets of parameters, exhibits strange attractors. Thus, both the dissipative and conservative behaviors exist in the same system with the switching of its parameter. Such behavior of a system is rarely reported in the literature. Further, the equilibria of the system are located on the surface-shape. The proposed system is implemented and simulated using Field Programmable Gate Array (FPGA) and Multisim simulation softwares.

Chaos theory and youth extremism in Russia

Many scientific works of sociologists, political analysts, psychologists, linguists have been devoted to the study of youth extremism, its various aspects and the fight against it. However, youth extremism still exists, and its violent manifestations destroy political and social stability in different countries including Russia. Therefore, the search for ways to counter this phenomenon continues. The purpose of the study is to clarify the concepts of youth extremism, to determine the approach to its study and the fight against it as well as to apply this approach to the predicted specific political crisis in Russia. Methodology, methods. The article uses chaos theory adapted to the analysis of social reality as a methodology for the study of youth extremism. To tackle manifestations of youth extremism, the method based on the use of so–called strange attractors is proposed. Results. The field of the research is determined through the correlation of the concepts of “extremism”, “radicalism”, “deviation”, “delinquency”. The study clarifies the concept of extremism, gives its classification, and substantiates the boundaries of its social carrier - the youth. Chaos theory is used to study youth extremism and predict the development of social crises in Russia, in which young people can take an active part. The possibility of using so-called strange attractors to prevent active performances of young extremists in a situation of a specific political crisis is shown. The scientific novelty lies in the use of chaos theory to study youth extremism in modern Russia and the fight against it. Practical significance. A concrete way of countering manifestations of youth extremism in real political conditions is suggested.

Strange Attractors in Writing Competence Development from the Perspective of Complexity Theory Based on Sensor Data

Writing competence is crucial for second language learners. Studying strange attractors in the development of writing competence is essential in understanding the laws of language development of foreign students. This study is aimed at investigating the state and laws of the development of Chinese as a second language (CSL) writing competence. Mathematical modeling and phase space construction methods in sensor research were used to investigate strange attractors in high-level Chinese learners studying in China in the development of CSL from the perspective of complexity theory based on the measurement framework of complexity, accuracy, and fluency. The results showed the following: (1) there are trends in the concentration and volatility of trigonometric function in different dimensions; (2) the group dynamic characteristics of writing development in CSL are simulated precisely by mathematical modeling; and (3) there are strange attractors with lexical density in CSL writing development. The development of CSL writing tends to maintain the state of strange attractors. The strange attractor reflects regularity in the dynamic, complex, and chaotic development of Chinese for international students, revealing the probabilistic prediction competence of different states in the development of CSL.

Torus-Breakdown Near a Heteroclinic Attractor: A Case Study

There are few explicit examples in the literature of vector fields exhibiting observable chaos that may be proved analytically. This paper reports numerical experiments performed for an explicit two-parameter family of [Formula: see text]-symmetric vector fields whose organizing center exhibits an attracting heteroclinic network linking two saddle-foci. Each vector field in the family is the restriction to [Formula: see text] of a polynomial vector field in [Formula: see text]. We investigate global bifurcations due to symmetry-breaking and we detect strange attractors via a mechanism called Torus-Breakdown. We explain how an attracting torus gets destroyed by following the changes in the unstable manifold of a saddle-focus. Although a complete understanding of the corresponding bifurcation diagram and the mechanisms underlying the dynamical changes is out of reach, we uncover complex patterns for the symmetric family under analysis, using a combination of theoretical tools and computer simulations. This article suggests a route to obtain rotational horseshoes and strange attractors; additionally, we make an attempt to elucidate some of the bifurcations involved in an Arnold tongue.

Statistical sustainability of a digital organization

An important feature of a digital organization is its ability to change rapidly. For an organization to remain capable of rapid change, it must be on the brink of resilience, since a resilient organization always resists change. The article examines the borderline state of the organization, which is on the verge of its stability and instability. In this state, the organization begins to lose predictability in the details of behavior, but still retains predictability in general. The authors called this borderline state the statistical sustainability of the organization. The phenomenon of statistical sustainability of an organization is very similar to the property of stability of the frequency of mass events and average values described in mathematical statistics by a similar term. To analyze the nature of the statistical sustainability of the organization, the authors used the ideas of strange attractors and modes with sharpening from the theory of complex systems. A strange attractor is an area of the organization’s behavior that, outside this area, is an area of stability for the organization, and inside it is an area of complete unpredictability. The theory of complex systems has shown that it is in the regions of strange attractors that the conditions for the variability of systems are created, and the theory of modes with aggravation shows the conditions under which this variability can lead to self-organization, that is, the spontaneous emergence of new structures. This article shows that systematic digitalization objectively leads to the formation of the statistical sustainability of the organization and creates the preconditions for maintaining the organization’s ability to make rapid changes. In traditional management, the statistical sustainability of an organization is viewed as a threat and a source of risk. Therefore, in the context of systematic digitalization, traditional approaches to management should be significantly refined.