The COVID-19 pandemic exhibited some interesting temporal dynamics that were not accounted for by the traditional susceptible-infectious-recovered (SIR) family of epidemic time series models. The recorded number of positive tests increased and declined in waves from March 2020 to October 2021. Additional variability appeared around the peak of the waves. The present study examined the time series of positive medical tests reported by the public health system for one U.S. State. The wave patterns were consistent with the probability density function associated with the swallowtail catastrophe model. The excess variability was hypothesized to be indicative of workload stress in the health care system. The analysis of residuals from the swallowtail model was consistent with the probability density function of the cusp catastrophe model, which is known as a viable model for changes in system performance under conditions of changing workload. The two functions together accounted for 96% of the variance in daily positive test reports. A chaotic model was also tested as an alternative to the cusp. Although it contained some informative dynamics, it was not as accurate as the cusp interpretation. Implications for modeling and forecasting future epidemics are discussed.

This study investigates the relationship between two phenomena that can emerge simultaneously in group interaction: autonomic synchrony and the emergence of leadership roles among team members. It was previously shown that the probability distributions of the two processes are both phase shifts characterized by the swallowtail catastrophe distribution. The objective of the present study was to examine the role of team autonomic synchrony as one of the three control parameters in the leadership emergence model. Research participants were 136 undergraduates who were organized into teams of three to five members playing the computer-game Counter-Strike while wearing GSR sensors. After approximately two hours of interaction, team members rated each other on leadership behaviors. Autonomic synchrony was analyzed as a driver-empath process that produces a group-level coefficient of synchrony (SE) from dyadic interactions from all possible dyadic interactions. The model was built in three stages: (a) replicate a model obtained from a similar team effort involving dynamic decisions, (b) test new variables as specific control parameters, and (c) test synchrony metrics for their best fit as one of the three control parameters. Results showed that both synchrony metrics were best understood as bifurcation variables that brought individuals who were already in the zone of potential leaders into primary or secondary roles. Prior gaming experience and SE Variability each played the role of a bias variable that distinguished between primary and secondary leaders. SE Variability also pre-empted team performance as a control variable.

Effective motor coordination is essential for adaptive athletic performance, including musculoskeletal injury prevention, particularly in high impact activities. Understanding how the lower extremities adapt to added constraints, such as increased load, can provide valuable insights into the resilience of movement patterns. This study examined the influence of added load on intralimb coordination during a drop-vertical jump (DVJ). Twenty-six participants (14 female, age = 23.10 +/- 3.97 years, 76.81 +/- 18.73kg) performed 5 body weight DVJs and 5 with an additional 25% body weight using a weighted vest. 3D joint kinematics were recorded using OpenCap markerless motion capture (OpenCap, Menlo Park, CA). Linear measures were calculated for the knee and hip, while nonlinear cross recurrence quantification analysis indexed intralimb coordination between the knee and hip joints. Alpha level was set a priori at α=.05. Paired-sample t-tests revealed smaller peak knee flexion (p=.013) and decreased total range of motion in both the hip and knee (p=.014 and .013, respectively) in the +25% body weight condition. Additionally, recurrence rate (p=.036), determinism (p=.046), adjusted mean line (p=.023), and adjusted trapping time (p=.011) were all lower in the +25% body weight condition. These results indicate that weight-based constraints lead to stiffer landing mechanics and noisier, less tightly coupled intralimb coordination. These findings highlight the need to consider both the landing mechanics and coordination dynamics when considering the implementation of movement assessments for athletic performance and injury prevention under increased load conditions.

The DARPA OP TEMPO program seeks to accelerate warfighter readiness by supplying instructors with objective, automatic assessments of team performance during simulation training. To that end, we created the Bio-behavioral Team Dynamics Measurement System (BioTDMS), a multimodal sensing and analytics pipeline that discovers bio-behavioral 'signatures' emanating from within the human body and through team-member interactions that predict team performance. BioTDMS employs a layered symbolic dynamics model that converts time-aligned neural, cardio-respiratory, eye tracking, and verbal data, collected using a multimodal sensor suite. Moving-window entropy and mutual information computed across the symbolic sensor space yield real-time metrics that quantify team adaptability following perturbation (e.g., 'training injects') and distribution of team members' influence across biological and behavioral subsystems. These features feed a multitask, multi-kernel learning engine that refines performance prediction while preserving explainability through team construct mapping and a command-line user interface. We present preliminary results from field testing a full physical and computational implementation of BioTDMS during Fire Support Team (FiST) training exercises at the U.S. Marine Corps Air-Ground Combat Center, Twentynine Palms, CA. An onsite team instrumented five-person FiST crews with multimodal sensor suites. Sensor data were processed by BioTDMS for real-time and post hoc analytics. BioTDMS currently accounts for 90â¯% of variance in a subjective team perform-ance assessment made by instructors, with improvements expected upon further refinements of BioTDMS modeling components. These findings demonstrate BioTDMS's potential as an operational tool for automatic, objective team assessments. Future assessments within air combat teams, including configura-tions with human-autonomy teaming, will evaluate the generalizability of BioTDMS.

This paper investigates the fate of original information after it is synthesized into knowledge, focusing on whether it becomes entangled within the integrated knowledge or if it is retained as isolated units in long-term memory. We explore two possibilities: either synthesized knowledge removes original information from memory, or both integrated and insulated information are stored once the information becomes part of knowledge. To address these questions, we simulate problem-solving processes over time. The simulation reveals how, once information is integrated into knowledge, it is removed as an insulated piece of information in the long-run memory. The process also shows a dynamic interplay between the creation and fragmentation of knowledge induced by synthetic and analytical skills. Furthermore, we examine whether the analytical-synthetic (A-S) process, as an autonomous system, tends to diverge or converge toward a steady state. We identify a stable stationary point in the process of knowledge creation and fragmentation. We also discuss how novelty can emerge exogenously (through errors) or endogenously and how it oscillates within the (A-S) process when heterogeneous information and knowledge are considered. Finally, we identify a chaotic transition in the way knowledge and theories compensate for reduced information.

We propose the novel hypothesis that Seasonal Affective Disorder (SAD), and seasonal mood variation more generally, may be influenced in part by how seasonal changes influence people's exposure to fractals in their environments - for example, due to changes in vegetation and cloud cover. This general hypothesis implies that seasonal mood variation may occur not only in high latitudes but also in tropical areas where wet-dry seasons alter the fractal character of the environment. Based on our general hypothesis, we develop a series of specific hypotheses about where seasonal mood variation may be most prevalent. We also discuss potential reasons for variation in mood across individuals and propose testable treatment options for those experiencing SAD.

This study evaluated autonomic synchrony and variability in synchrony as control variables in cusp catastrophe models of workload and fatigue for teams making dynamics decisions. In this experiment, 136 undergraduates were organized into 32 groups of three, four, and five members playing an online computer game while wearing electrodermal sensors. They also completed cognitive measures of elasticity-rigidity and situation awareness during the games. Synchrony was calculated using the SE coefficient from the driver-empath model. Analyses were constructed to determine whether SE or SE variability added value to the cusp catastrophe models for cognitive workload and fatigue that were determined previously in Guastello and McGuigan (2024). Results indicated that SE made a strong impact on changes in performance as a bifurcation variable in both the workload and fatigue models. The positive and negative impact on performance shown by SE variability suggested that team members were grappling with the best ways to coordinate with each other or that teams found an advantage to turning synchrony on and off. SE variability made a strong impact as a bifurcation variable in the workload load model, and a strong impact as a compensatory ability (asymmetry parameter) in the fatigue model. Practical implications are that synchrony could be functional or dysfunctional, depending on situational demands that could be momentary. The study opened new questions regarding the qualitative relationship between elasticity-rigidity variables and synchrony and the possible roles of strong vs. weak ties in a closed network of this type.

The present research develops a formal mathematical model to measure individual motivation at work. Its mathematical specifications correspond to a formal translation of Conservation of Resources (COR) theory core assumptions. It explores how such COR constructs as resource caravan and resource passageway determine patterns of motivational processes. The model is applied to a sample of working professionals (n = 8) from different occupations. Data is obtained from a 5-item Likert-scale questionnaire based on the COR-Evaluation (COR-E) instrument developed by Hobfoll et al. (1992). Results are presented in the form of eight tables that correspond to eight different resource caravans. They unveil how individual motivational processes vary by the extent to which resources interact with an underlying drive for preservation. The role of context is also confirmed as a resource passageway. With regard to methodology, this research emphasizes how measurement based on mathematical modeling can be an alternative to standard data-analytic statistics. At a theory level, it enriches both COR-based literature and theory of workplace motivation. Practically, it provides an analytical instrument that details information on those processes that shape individual motivational profiles in organizations.

In this paper we introduce a mathematical model of psychotherapy where the proposed continuous dynamical system describes the relationship between the client and the therapist based on dyadic interactions modeling. The model also incorporates the influence representing the external environment of the client's state. It was assumed that given that influence is negative. In order to reflect possible instability of the client's state, we describe the client who can demonstrate other mental comorbidities. Additionally, this assumption depicts the fact that his/her preferable state can be not unique. We analyse basic properties of the model and use it to study various scenarios of final results of psychotherapy.

This article discusses the spreading model of addicted smoking involving five compartments, namely susceptible, addicted, temporary quitters, permanent quitters, and not interested in smoking. This model is expressed as a system of nonlinear ordinary differential equations. Parental guidance and anti-nicotine therapy are considered in the model as strategies to control and prevent the spread of addicted smoking. Addicted and non-addicted fixed points of the model are analyzed using linearization, eigenvalues, the Routh-Hurwitz test, and the basic reproduction number. Sensitivity analysis of the model parameters to the basic reproduction number was carried out to determine the influence of the parameters, and it was found that the transmission rate has a significant contribution to the spread of addicted smoking. The model with control is then related to the problem of minimizing the number of individuals addicted to smoking. By using the Pontryagin minimum principle, an optimal path is obtained that minimizes the number of individuals addicted to smoking in a specific time interval. The simulation used several assumptions and model parameter values estimated from actual data. From the optimal path with and without controls, it was found that both controls significantly reduced the number of individuals addicted to smoking.

Using two different complex mathematical models, a number of fractal images with interesting aesthetic values were computer generated. Due to their similarity to real objects, they were given names. Both the state variables of individual models and the values of their Lyapunov exponents were used as a criterion for creating these images.

In this article we model two-strain dynamics of dengue transmission by both mosquitoes and humans with vertical transmission to larvae in the mosquito population. We include secondary infections, causing a severe form of disease. Mathematical analysis of proposed model is conducted - we study existence and local stability of equilibria of the system. While analysing the model, unusual properties emerged which lead us to implement its simplifications and obtain different results. Theoretical outcomes are accomplished with numerical simulations. They suggest that vertical transmission has a negligible impact on the dengue spread.

Psychotherapy is a dynamic, two-person process involving the complex interplay between a client and therapist. Recent perspectives conceptualize psychotherapy as a complex dynamic system, integrating biological, psychological, and social factors. Research suggests that the psychotherapeutic process can be unpredictable, fluctuating, and erratic. To capture this complexity, mathematical models have been developed. One such model, a two-dimensional representation of psychotherapy timing and emotional valence, focuses on the valence (positive or negative emotional tone) of both client and therapist. Incorporating delayed reactions from both parties, the model employs delayed differential equations. This modification enables the emergence of complex dynamics, potentially exhibiting chaotic behavior characterized by a positive Lyapunov exponent. The interplay between delayed reactions and therapist distress of the client-therapist alliance drives these chaotic dynamics. Our findings have significant implications for understanding the psychotherapy process, highlighting the importance of temporal factors and therapeutic relationships.

The articles in this special issue examine the contributions of Jeffrey A. Goldstein to the understanding of emergence as a formal group of processes. Applications include work teams, organizations, ecologies of organizations, and societies. Prominent methodologies include agent-based modeling, qualitative analysis of publicly available business and governmental reports, structured analyses of team discussions, and nonlinear statistical analysis of time series data.

Emergence as a phenomenon is embedded and expressed in the natural world, and in social systems. Introduced nearly 150 years ago in a philosophical context, it has since been applied in nearly every natural and social science. However all of these uses are not congruent, as the range of emergences in this Special Issue reflect as well; this has limited the accumulation of knowledge about emergence, as well as its development as a discipline. The present paper attempts to bring coherence to emergence, by identifying its core characteristics, its primary expressions, and key principles of emergence. Much of the effort is based on the work of Jeffrey Goldstein, who was one of the first to examine the conceptual, mathematical, and social implications of emergence. The article concludes by showing how a science of emergence can be usefully applied to leadership, and entrepreneurship.

This article analyzes the research career of Jeffrey Goldstein from the perspective of nonlinear dynamical systems. Goldstein's focus was on the application of emergence in complex social systems. He applied emergence to issues in organizational development, leadership, social entrepreneurship, and innovation. The study uses qualitative methods to identify the stages and corresponding research themes within Goldstein's publications over time. These stages are qualitatively characterized as representing either convergent or divergent activities. Goldstein's research career dynamics suggest that the way he managed his career was different from other academics and helps explain his significant influence on other researchers. Goldstein's primary epistemology was dialectics, and he followed a philosophy of engaged scholarship. His 'self-transcending constructions,' which stood in contrast to the concept of self-organization, was the invention that continues to differentiate Goldstein's work from other complexity scientists. Goldstein's change in foci later in his career to the service of social change and his institution building to the benefit of others suggests Goldstein was a mensch.

Emergent phenomena exhibit interesting dynamics when considered individually. The present article examines two emergent processes that could be occurring simultaneously in an intense team interaction: the emergence of leaders and the emergence of autonomic synchrony within teams making dynamic decisions. In the framework of panarchy theory and related studies on complex systems, autonomic synchrony would be a fast dynamic that is shaped or controlled by leadership emergence, which is a slower dynamic. The present study outlines three distinct statistical distributions - the swallowtail catastrophe model for phase shifts, inverse power laws that indicate fractal processes, and lognormal distributions - that are known to characterize emergent processes of different types. The objective was to determine the extent to which the two emergent processes reflected the same dynamics. Research participants were 136 undergraduates who were organized into teams of three to five members playing the computer-game Counter-Strike while wearing GSR sensors to measure autonomic arousal levels in a steady stream. After approximately two hours of interaction, team members rated each other on leadership behaviors. Autonomic synchrony was analyzed as a driver-empath process that produced individual driver scores (the total influence of one person on the rest of the group) and empath scores (the total influence of the group on one person). Results showed that leadership emergence displayed the swallowtail configuration that was consistent with prior studies. Autonomic synchrony started as a simpler process and unfolded into a swallowtail catastrophe toward the end of the experimental session. Lognormal distributions were second-best representations of all variables. Inverse power laws were least descriptive of any of the research variables. The implications of the temporal dynamics of the co-emerging processes for training and team development are discussed.

Besides consultants and practitioners, some contributions in the organizational economics literature have advocated substituting internal firms' bureaucracies with markets to regulate internal transactions. However, usually the effects of competition on performance are considered in terms competition across firms or industries. By contrast, other contributions point out that competition is pervasive inside firms as well. In this paper, we assume that conflict is directly related to the level of competition and propose a model which analyze the dynamics of performance when the manager decides the level of competition observing the group performance. We study the stability of the equilibria and analyze the bifurcations. We show that the fixed point with null performance is a Milnor attractor, and this may suggests why any attempt to move from this unsatisfactory outcome is unsuccessful.

We model an adaptive agent-based environment using selfish algorithm agents (SA-agents) that make decisions along three choice dimensions as they play the multi-round prisoner's dilemma game. The dynamics that emerge from mutual interactions among the SA-agents exhibit two collective-level properties that mirror living systems, thus making these models suitable for societal/biological simulation. The properties are: emergent intelligence and collective agency. The former means there is observable intelligent behavior as a unitary collective entity. The latter means the collective exhibits observable adaptability that enables it to reorganize its network structure to meet its objectives in response to a changing environment. In this study, we generate these capabilities in a single, simple case. We do this first by letting a temporal complex network among SA-agents emerge and second by changing conditions in the ecosystem to test adaptability. This latter phase is done by introducing an artificial virus that infects SA-agents during interactions and can remove (or 'kill') the SA-agents. We then study the dynamics of the contagion within the collective as the virus spreads through the population and impacts collective reward-seeking performance. Specifically, we compare two strategies to control the spread of the virus: exogenous top-down control and endogenous bottom-up self-isolation strategies.

This study takes a phenomenon-based framework and the self-transcending constructions approach to explain why wicked human services problems need to be addressed differently than wicked social-ecological problems. Based on the study's findings, a new approach for addressing wicked human services problems is proposed. In Australia, a Systemic Innovation Lab approach that incorporates a customized software tool has been used to address social-ecological wicked problems. Both, the lab approach and the software tool are based on a framework that is underpinned by dissipative structures and self-transcending constructions theories. This article uses a phenomenon-based approach, as well as insights from self-transcending constructions theory, to discuss why the Systemic Innovation Lab approach and its software tool have not been utilised to address wicked human services problems. This is because when addressing wicked human services problems, the containing, constraining and constructional operations of self-transcendent construction are different than those for wicked social-ecological problems. The results also suggest the need for new software tools to satisfy disability accessibility standards. In response to these identified needs, the article argues that a Systemic Landscape of Practice Lab approach which incorporates a spreadsheet tool that satisfies disability accessibility standards is needed to address wicked human services problems.

Theories and studies of ecosystem emergence focus on macro level explanations such as government investments in research and development or those at the organizational level such as displacement of an older technological system by a new one through competition between technologies. However, mechanisms by which such shifts occur are underemphasized. This article draws on complexity theory to develop a theoretical framework to describe how emergence is generated through top down 'rules' that constrain the behavior of the system, directing it towards a desired outcome. Emergence dynamics include rules to encourage participants (including entrepreneurs and established organizations) to exploit opportunities arising from disequilibrium conditions. Amplifying actions arise from support for the emerging ecosystem, followed by recombination of the elements of the system to enable integration. The system stabilizes when it achieves a level of performance and legitimacy. Findings from a case study on the emergence of the Indian renewable energy ecosystem support the framework and provide policy implications for designing ecosystems.