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Most economic concepts such as the market, competition, flexibility, pricing of production factors and consumption theory no longer reflect the reality of the contemporary situation. The current economic model and political system form a synthesis of fiduciary economics and privilege political systems. The exponential rise in material wealth amassed over the industrial age is unsustainable when figuring in the availability of resources. Even more interesting is how it may run counter to human instincts, our gene structure, and how the mindset and behavioral pattern are forged. As the economy and society evolves, combining in-depth knowledge across various disciplines is crucial to furthering our understanding of the world.

Managers are faced with increased complexity and unexpected risks. This article raises some reasons for the increase in complexity and risks. It also describes the tools and approaches used to anticipate some of these risks and how to mitigate against them. The usefulness of the scenario planning process is also indicated. The type of behavioral biases that makes risk identification difficult is also explained.

In this paper, we propose a new method of Rényi entropy and surrogate data analysis as a new measure to assess the complexity of a complex dynamical system. Simulations are conducted over artificial sequence and stock market series to provide model test and empirical analysis. The results show that the new method has a strong identification for different series and the $\mathrm{\Delta }R(q)$ curves of stock markets are all successfully fitted by exponential functions. These results can be well identified and analyzed in depth.

Legs are the contact point of humans during walking. In fact, leg muscles react when we walk in different conditions (such as different speeds and paths). In this research, we analyze how walking path affects leg muscles’ reaction. In fact, we investigate how the complexity of muscle reaction is related to the complexity of path of movement. For this purpose, we employ fractal theory. In the experiment, subjects walk on different paths that have different fractal dimensions and then we calculate the fractal dimension of Electromyography (EMG) signals obtained from both legs. The result of our analysis showed that the complexity of EMG signal increases with the increment of complexity of path of movement. The conducted statistical analysis also supported the result of analysis. The method of analysis used in this research can be further applied to find the relation between complexity of path of movement and other physiological signals of humans such as respiration and Electroencephalography (EEG) signal.

In this research, for the first time, we analyze the relationship between facial muscles and brain activities when human receives different dynamic visual stimuli. We present different moving visual stimuli to the subjects and accordingly analyze the complex structure of electromyography (EMG) signal versus the complex structure of electroencephalography (EEG) signal using fractal theory. Based on the obtained results from analysis, presenting the stimulus with greater complexity causes greater change in the complexity of EMG and EEG signals. Statistical analysis also supported the results of analysis and showed that visual stimulus with greater complexity has greater effect on the complexity of EEG and EMG signals. Therefore, we showed the relationship between facial muscles and brain activities in this paper. The method of analysis in this research can be further employed to investigate the relationship between other human organs’ activities and brain activity.

The rapid and accurate diagnosis of power grid faults plays a vital role in speeding up the process of accident handling and system recovery and ensuring the safe operation of the power system. This paper proposes to apply the ensemble empirical mode decomposition (EEMD) method and scale-related intrinsic entropy to diagnose the type of fault for the transmission line. First, the electrical data collected by the power system is decomposed by using the EEMD method. Then by eliminating some intrinsic mode functions, the signal is reconstructed by inspecting the correlation coefficient. Finally, the complexity of the reconstructed signal is calculated by using the scale-dependent intrinsic entropy. Since the scale-dependent intrinsic entropy reflects the complexity of one-dimensional time series, it is susceptible to signal changes. The complexity is helpful in the power system for fault signal analysis. The results show the combined method’s effectiveness and practicability through failure analysis using the IEEE 14-bus system as the simulation model.

We derive a sum rule that constrains the scale based decomposition of the trajectories of finite systems of particles. The sum rule reflects a tradeoff between the finer and larger scale collective degrees of freedom. For short duration trajectories, where acceleration is irrelevant, the sum rule can be related to the moment of inertia and the kinetic energy (times a characteristic time squared). Thus, two nonequilibrium systems that have the same kinetic energy and moment of inertia can, when compared to each other, have different scales of behavior, but if one of them has larger scales of behavior than the other, it must compensate by also having smaller scales of behavior. In the context of coherence or correlation, the larger scale of behavior corresponds to the collective motion, while the smaller scales of behavior correspond to the relative motion of correlated particles. For longer duration trajectories, the sum rule includes the full effective moment of inertia of the system in space-time with respect to an external frame of reference, providing the possibility of relating the class of systems that can exist in the same space-time domain.

One impact of the introduction of television, according to widely held views, is an undermining of traditional values and social organization. In this study, we simulate this process by representing social communication as a Random Boolean Network in which the individuals are nodes, and each node's state represents an opinion (yes/no) about some issue. Television is modelled as having a direct link to every node in the network. Two scenarios were considered. First, we found that, except in the most well connected networks, television rapidly breaks down cohesion (agreement in opinion). Second, the introduction of Hebbian learning leads to a polarizing effect : one subgroup strongly retains the original opinion, while a splinter group adopts the contrary opinion. The system displays criticality with respect to connectivity and the level of exposure to television. More generally, the results suggest that patterns of communication in networks can help to explain a wide variety of social phenomena.

Complex systems are of vast importance in the practical world as well as presenting many theoretical challenges. The measurement of system complexity is still imprecise. For many systems, their modular construction brings challenges in understanding how modules form and the emergent behavior which may result. In other systems, it is the development of encodings and communication protocols which allow complexity to increase dramatically. We take a broad view of these issues and then consider the nature of the system space which generates complexity. We show examples from cellular automata and applications of neural networks to data mining which suggest that complex systems often occupy simple structured sub-spaces. Finally, we look at the way modularity relates to networks and the implications for understanding human cognitive processing.

We discuss the role of scale dependence of entropy/complexity and its relationship to component interdependence. The complexity as a function of scale of observation is expressed in terms of subsystem entropies for a system having a description in terms of variables that have the same a priori scale. The sum of the complexity over all scales is the same for any system with the same number of underlying degrees of freedom (variables), even though the complexity at specific scales differs due to the organization/interdependence of these degrees of freedom. This reflects a tradeoff of complexity at different scales of observation. Calculation of this complexity for a simple frustrated system reveals that it is possible for the complexity to be negative. This is consistent with the possibility that observations of a system that include some errors may actually cause, on average, negative knowledge, i.e. incorrect expectations.

We analyze how difficult it is to synchronize to a periodic sequence whose structure is known, when an observer is initially unaware of the sequence's phase. We examine the transient information T, a recently introduced information-theoretic quantity that measures the uncertainty an observer experiences while synchronizing to a sequence. We also consider the synchronization time τ, which is the average number of measurements required to infer the phase of a periodic signal. We calculate T and τ for all periodic sequences up to and including period 23. We show which sequences of a given period have the maximum and minimum possible T and τ values, develop analytic expressions for the extreme values, and show that in these cases the transient information is the product of the total phase information and the synchronization time. Despite the latter result, our analyses demonstrate that the transient information and synchronization time capture different and complementary structural properties of individual periodic sequences — properties, moreover, that are distinct from source entropy rate and mutual information measures, such as the excess entropy.

The effects of periodic forcing and impulsive perturbations on the predator–prey model with Beddington–DeAngelis functional response are investigated. We assume periodic variation in the intrinsic growth rate of the prey as well as periodic constant impulsive immigration of the predator. The dynamical behavior of the system is simulated and bifurcation diagrams are obtained for different parameters. The results show that periodic forcing and impulsive perturbation can very easily give rise to complex dynamics, including quasi-periodic oscillating, a period-doubling cascade, chaos, a period-halving cascade, non-unique dynamics, and period windows.

In this paper, we investigate the extinction, permanence and dynamic complexity of the two-prey, one-predator system with Ivlev's functional response and impulsive perturbation on the predator at fixed moments. Conditions for the extinction and permanence of the system are established via the comparison theorem. Numerical simulations are carried out to explain the conclusions we obtain. Furthermore, the resulting bifurcation diagrams clearly show that the impulsive system takes on many forms of complexity including period-doubling bifurcation, period-halving bifurcation, and chaos.

In this paper, we consider a predator–prey chemostat model with ratio-dependent Monod type functional response and periodic input and washout at different fixed times. We obtain an exact periodic solution with substrate and prey. The stability analysis for this periodic solutions yields an invasion threshold for the period of pulses of the predator. When the impulsive period is more than the threshold, there are periodic oscillations in the substrate, prey, and predator. If the impulsive period further increases, the system undergoes a complex dynamic process. By analyzing bifurcation diagrams, we can see that the impulsive system shows two kinds of bifurcation, which are period-doubling and period-halving.

This paper discusses the debate between those advocating a computational and those advocating a dynamic definition of complexity, and how this relates to issues in econophysics. It then reviews the criticisms that have been raised about ways in which econophysics has been done, noting that many of these are now being dealt with. Finally, it argues that while an obvious way to resolve many of these matters is to have economists and physicists work together, the physicists should be sure to work with economists who understand the complexity critique of conventional economic theory and are thus not led astray into building models that have some of the problems of standard economics models that most econophysicists have striven to overcome.

We use an ecosystem simulator capable of evolving arbitrary neural network topologies to explore the relationship between an information theoretic measure of the complexity of neural dynamics and several graph theoretical metrics calculated for the underlying network topologies. Evolutionary trends confirm and extend previous results demonstrating an evolutionary selection for complexity and small-world network properties during periods of behavioral adaptation. The resultant mapping of the space of network topologies occupied by the most complex networks yields new insights into the relationship between network structure and function. The highest complexity networks are found within limited numerical ranges of clustering coefficient, characteristic path length, small-world index, and global efficiency. The widths of these ranges vary from quite narrow to modest, and provide a guide to the most productive regions of the space of neural topologies in which to search for complexity. Our demonstration that evolution selects for complex dynamics and small-world networks helps explain biological evidence for these trends and provides evidence for selection of these characteristics based purely on network function—with no physical constraints on network structure—thus suggesting that functional and structural evolutionary pressures cooperate to produce brains optimized for adaptation to a complex, variable world.

The paper studies which incentive systems emerge in organizations when self-interested managers collaboratively search for higher levels of organizational performance and the headquarters learn about the success of the incentive systems employed. The study uses an agent-based simulation and, in particular, controls for different levels of intra-organizational complexity and modes of coordination, i.e., the way how preferences on the departmental site are aligned with each other in respect to the overall organizational objective. The results indicate that for different levels of intra-organizational complexity different incentive systems emerge: With lower intra-organizational complexity, in tendency, the less focus is put on firm performance and vice versa. However, results also suggest that the mode of coordination may considerably affect the emergence of the incentive structure. This provides support for the idea that multiple management controls, like the incentive system and the mode of coordination, should be regarded and designed as a system with interrelations among its components and not just as a collection of several control practices.

There is a public and scholarly debate about whether personalized services of social-media platforms contribute to the rise of bipolarization of political opinions. On the one hand, it is argued that personalized services of online social networks generate filter bubbles limiting contact between users who disagree. This reduces opportunities for assimilative social influence between users from different camps and prevents opinion convergence. On the other hand, empirical research also indicated that exposing users to content from the opposite political spectrum can activate the counter-part of assimilative influence, repulsive influence. Fostering contact that leads to opinion assimilation and limiting contacts likely to induce repulsive interactions, it has been concluded, may therefore prevent bipolarization. With an agent-based model, we demonstrate here that these conclusions fail to capture the complexity that assimilative and repulsive influence generate in social networks. Sometimes, more assimilative influence can actually lead to more and not less opinion bipolarization. Likewise, increasing the exposure of users to like-minded individuals sometimes intensifies opinion polarization. While emerging only in specific parts of the parameter space, these counter-intuitive dynamics are robust, as our simulation experiments demonstrate. We discuss implications for the debate about filter bubbles and approaches to improve the design of online social networks. While we applaud the growing empirical research on the micro-processes of assimilative and repulsive influence in online settings, we warn that drawing conclusions about resulting macro-outcomes like opinion bipolarization requires a rigorous analysis capturing the complexity of online communication systems. Intuition alone is error-prone in this context. Accordingly, models capturing the complexity of social influence in networks should play a more important role in the design of communication systems.

Theoretical and computational frameworks of complexity science are dominated by binary structures. This binary bias, seen in the ubiquity of pair-wise networks and formal binary operations in mathematical models, limits our capacity to faithfully capture irreducible polyadic interactions in higher-order systems. A paradigmatic example of a higher-order interaction is the Borromean link of three interlocking rings. In this paper, we propose a mathematical framework via hypergraphs and hypermatrix algebras that allows to formalize such forms of higher-order bonding and connectivity in a parsimonious way. Our framework builds on and extends current techniques in higher-order networks — still mostly rooted in binary structures such as adjacency matrices — and incorporates recent developments in higher-arity structures to articulate the compositional behavior of adjacency hypermatrices. Irreducible higher-order interactions turn out to be a widespread occurrence across natural sciences and socio-cultural knowledge representation. We demonstrate this by reviewing recent results in computer science, physics, chemistry, biology, ecology, social science, and cultural analysis through the conceptual lens of irreducible higher-order interactions. We further speculate that the general phenomenon of emergence in complex systems may be characterized by spatio-temporal discrepancies of interaction arity.

Bibliometric studies based on the Web of Science (WOS) database have become an increasingly popular method for analyzing the structure of scientific research. So do network approaches, which, based on empirical data, make it possible to characterize the emergence of topological structures over time and across multiple research areas. Our paper is a contribution to interweaving these two lines of research that have progressed in separate ways but whose common applications have been increasingly frequent. Among other attributes, Author Keywords and Keywords Plus® are used as units of analysis that enable us to identify changes in the topics of interest and related bibliography. By considering the co-occurrence of those keywords with the Author Keyword Complexity, we provide an overview of the evolution of studies on Complexity Sciences, and compare this evolution in seven social and natural scientific fields. The results show a considerable increase in the number of papers dealing with complexity, as well as a general tendency across different disciplines for this literature to move from a more foundational, general and conceptual to a more applied, specific and empirical set of co-occurring keywords. Moreover, we provide evidence of changing topologies of networks of co-occurring keywords, which are described through the computation of some topological coefficients. In so doing, we emphasize the distinguishing structures that characterize the networks of the seven research areas.