Narrow Results

From the perspective of mathematical epidemiology, COVID-19 epidemics emerge due to instabilities in epidemiological systems. It is shown that the COVID-19 outbreaks follow highly specified paths in epidemiological state spaces. These paths are described by phase portraits that can be readily computed from epidemiological models defined in terms of nonlinear dynamical systems. The paths are predicted by order parameters and amplitude equations that are well known in nonlinear physics and synergetics to exist at instability points. The approach is illustrated for SIR, SEIR and SEIAR models and epidemic outbreaks in China, Italy and West Africa. Identifying such COVID-19 order parameters may help in forecasting COVID-19 epidemics and predicting the impacts of intervention measures.

Many scientists have struggled to uncover the elusive origin of "complexity", and its many equivalent jargons, such as emergence, self-organization, synergetics, collective behaviors, nonequilibrium phenomena, etc. They have provided some qualitative, but not quantitative, characterizations of numerous fascinating examples from many disciplines. For example, Schrödinger had identified "the exchange of energy" from open systems as a necessary condition for complexity. Prigogine has argued for the need to introduce a new principle of nature which he dubbed "the instability of the homogeneous". Turing had proposed "symmetry breaking" as an origin of morphogenesis. Smale had asked what "axiomatic" properties must a reaction–diffusion system possess to make the Turing interacting system oscillate.

The purpose of this paper is to show that all the jargons and issues cited above are mere manifestations of a new fundamental principle called local activity, which is mathematically precise and testable. The local activity theorem provides the quantitative characterization of Prigogine's "instability of the homogeneous" and Smale's quest for an axiomatic principle on Turing instability.

Among other things, a mathematical proof is given which shows none of the complexity-related jargons cited above is possible without local activity. Explicit mathematical criteria are given to identify a relatively small subset of the locally-active parameter region, called the edge of chaos, where most complex phenomena emerge.

This paper reports that synergetics are used to analyze the crazing evolution. On this basis, chaotic effect is explored. The chaos equation is established and verified. The theoretical derivation are consistent with the experimental results. We design a special specimen with a special loading mode, the transient monitoring function of acoustic emission (AE) technology is used to track and detect the crazing inside the PMMA in real time, and the experiments show that synergetics can explain the crazing properties of polymer. Importantly, the mathematical explanation is also given. The AE analysis, synergetics, and craze photo reached a conclusion that the crazing has chaotic behavior. After analyzing the AE events and crazing at different stress levels, the accuracy of synergetic approach for crazing is verified. By studying the course of AE events and crazing, the self-organization effect is proposed. The research results will provide data support for the application of PMMA in ship, aircraft, and precision instruments.

A model for gait transitions from walking to running is proposed. The model is based on the theory of pattern formation and synergetics. Walking and running are considered as spatiotemporal patterns, while walk-to-run and run-to-walk transitions are regarded as bifurcations. Consequently, the model is cast in the form of coupled amplitude equations as known in the literature on pattern formation. It is shown that the model can reproduce hysteretic gait transitions that have been observed in experimental studies with humans walking on treadmills when locomotion speed is gradually increased and decreased. The control parameter is an appropriately rescaled velocity measure, the so-called Froude number, which is a body-scaled parameter that takes leg length into account. It is shown that the model can reproduce observed gait transitions for individuals and populations. In particular, probabilistic functions describing gait transitions on the population level can be defined that resemble the experimentally determined probabilistic function.

From a dynamical systems perspective, COVID-19 infectious disease emerges via an instability in human populations. Accordingly, the human population free of COVID-19 infected individuals is an unstable state and the dynamics away from that unstable state is a bifurcation. Recent research has determined COVID-19 relevant bifurcation parameters for various countries in terms of basic reproduction ratios. However, little is known about the relevant order parameters (synergetics) of COVID-19 bifurcations and the corresponding time constants. Those order parameters describe directions in compartment model spaces in which infection dynamics initially evolves. The corresponding time constants describe the speed of the dynamics along those directions. COVID-19 order parameters and their time constants are derived within a standard SEIR dynamical systems framework and determined explicitly for two published studies on COVID-19 trajectories in Italy and China. The results suggest the existence of certain relationships between order parameters, time constants, and reproduction ratios. However, the examples from Italy and China also suggest that COVID-19 order parameters and time constants in general depend on regional differences and the stage of the local COVID-19 epidemic under consideration. These findings may help to improve the forecasting of COVID-19 outbreaks in new hotspots around the world.

COVID-19 confronts societies and individuals with unprecedented challenges. It is advocated that complex systems theory, in general, and synergetics, in particular, provide a valuable and comprehensive repertoire of tools and concepts such as the concept of amplitude equations and order parameters to study the spread of COVID-19 in human populations. Specifically, within the framework of SIR and SEIR compartment models COVID-19 trajectories are described in terms of amplitude equations and order parameters. By plotting simulated and semi-empirical COVID-19 case trajectories it is shown that the initial epidemics in China, in general, and Wuhan city, in particular, during the first quarter of the year 2020 followed relatively simple amplitude dynamics in SIR and SEIR model state spaces describing interaction classes of individuals. The amplitudes evolve along certain paths or directions determined by order parameters that are well known to exist in complex systems. In summary, the present work highlights that COVID-19 outbreaks are constrained by general principles that hold for a broad class of phenomena in living and non-living systems.

The inherent micro-structure (agent-agent/system) of human organizations has been introduced in Chapters 2 and 3. Fundamentally, human organizations are composite complex adaptive systems with human beings as interacting agents (each an intrinsic complex adaptive system). This chapter further analyzes the basic conceptual foundation of the multi-layer structure, including advantages of the intelligent biotic macro-structure (with inherent features similar to that of an intelligent biological being — a structural reform), and its unique and more integrative complex adaptive dynamic in intelligent human organizations (towards iCAD). The necessity of nurturing an intelligent biotic macro-structure with vital characteristics that better synchronize and enhance sophisticated information/knowledge-related activities is highly beneficial — achieving a higher structural capacity. Thus, the attributes, functions and higher structural capacity of the more intelligent biotic macro-structure can reinforced the competitiveness of any categories of human organizations extensively.

In this respect, connecting and engaging of intelligence/consciousness sources (individual and collective), organizing around intelligence, intelligence/ consciousness management, and the intelligent biotic macrostructure are mutually enhancing (towards higher coherency). Apparently, being intelligence/consciousness-centric is a beneficial and critical activator (strategic foundation) of the intelligence paradigmatic shift. In the present context, the roles and integration of intelligence, information and knowledge, as well as nurturing a ‘common’ language and elevating coherency in human organizations (with respect to the macro-structure and micro-structure, as well as their higher collectiveness — collectiveness capacity) must be more deeply scrutinized and utilized. The presence and significance of the individual intelligence enhancer encompassing three entities namely, intelligence, knowledge, and theory in the human thinking systems, and the necessity of nurturing a similar and effective intelligence enhancer at organizational level are analyzed. Subsequently, the supporting roles and contributions of artificial intelligence systems are also examined.

In between the macro-structure and micro-structure are two meso-structures. In the intelligent organization theory, the complexity meso-structure encompasses spaces of complexity and punctuation points. In this respect, complexity is a highly significant focal point, and the exploitation of co-existence of order and complexity is a new necessity (complexity-centricity). Next, the network meso-structure encompassing complex network (network of networks) is also an inherent structure and dynamic in all human organizations. This meso-structure is briefly introduced, and will be more deeply analyzed with respect to governance (network-centricity, network governance).

Hence, it is crucial to lead and manage human organizations with a strategic approach that integrates the above multi-layer structure/ dynamic at all time so that a higher structural capacity, collectiveness capacity, adaptive capacity, self-organizing capacity, and emergence-intelligence capacity can be nurtured. In the current highly competitive context, possessing these positive capabilities to elevate coherency and synergetic characteristics (including social consensus and the construal aspect) and dynamic is also highly crucial — a key focus of the complexity-intelligence strategy (towards achieving higher organizational mental cohesion). Hence, the significance and impact of nurturing intelligent human organizations with the complexity-intelligence-centric and network-centric approach that leads to the emergent of smarter evolvers and emergent strategists must be better understood and adopted. (The conceptual foundation on structural-dynamic coherency and synergy in intelligent human organizations developed in this chapter will be more deeply reviewed and exploited in later chapters.)

Our environment, such as natural, social, economics and engineering ones are the world of complex supersystems of various natures. These systems are a collection of various subsystems providing defined functions and interconnected by processes of forced dynamics interaction and exchange of power, matter and information. These supersystems are nonlinear, multidimensional and multilinked. And in these systems are complex transients and have place of critical and chaotic modes. Problems of system synthesis, i.e. finding of common objective laws of control processes in such a dynamics system are much actual, complicated and, in many respects, practically inaccessible for present control theory.

In the report we consider fundamental basis of nonlinear theory of system's synthesis based on synergetics approach in modern control theory as well as its application [1, 2].

The report consists of three parts: Part I General statements; Part II Strategies of synergetics control; Part III Synergetics synthesis of nonlenear systems with state observers.