3333 Week 11

Nonlinear Dynamics in Psychology and Life Science

• Constraints on behavioral variability can either increase or decrease deterministic structure, as indicated by the color-coded graph.
• Complexity matching in coupled human behavioral variability involves correlated fractal structures and can be observed between individuals with different levels of behavioral structure.
• Complexity matching in the wild, as studied by Rigoli et al. in 2020, shows that the fractal structure of an individual's movements differs for different tasks, but complexity-matching between individuals completing a task together remains invariant to the task or task goal.
• Social motor coordination involves interpersonal and intrapersonal interlimb coordination, which can exhibit coupled periodic/rhythmic behaviors.
• Manipulated competition in social motor coordination, such as attaching weights to chairs, can lead to different relative phase occurrences between individuals, indicating different levels of coupling strength.
• Harmonious interactions, rapport, and social connection can be achieved through social motor coordination, as evidenced by various studies.
• Group status manipulation through "art preference" categorization affects the relative phase occurrences in social motor coordination tasks.
• Competitive running and sprinting coordination can be studied to determine stride coordination, as seen in the example of Usain Bolt and Tyson Gay in the 100-m final of the 12th IAAF World Championship in Athletics.
• A dynamical system is formally defined as a set of rules or equations that determine the future state of a system given its current state, and a state can represent various characteristics or measurements.
• A computational dynamical system example is provided, illustrating how the future states of a system at discrete time steps can be determined using a set of rules or equations.
• Simple rules can result in complex, unpredictable behavior, as demonstrated by the logistic equation and the conditions under which chaos occurs.
• Chaos in human behavior is characterized by unpredictable yet deterministic behavior, which is aperiodic, bounded, and exhibits a sensitive dependence on initial conditions.

Complex Dynamical Systems: Key Aspects and Examples

• Complex systems involve a large number of interacting components or agents.
• The dynamics of complex systems are nonlinear, meaning outputs are not directly proportional to inputs.
• Emergence and self-organization are key features of complex systems, with behaviors depending on context and local interactions.
• Examples of emergence and self-organization include coordinated activities of social insects and flocking behaviors.
• Craig W. Reynold's Flocking Model demonstrates rules for simulated flocking behavior.
• Dynamical human behavior and fractal time-series data exhibit complex time- and event-series dynamics.
• Stochastic behaviors, such as self-esteem fluctuations, are part of human behavioral variability.
• Fractal structures in human behavioral variability exhibit self-similar or scale-invariant structures.
• Human behavioral variability exhibits fractal dynamics, characterized by persistent, anti-persistent, and random fluctuations.
• Pink or fractal noise is characteristic of adaptive, flexible, and robust human and animal behavior at various scales.
• Fluctuations in self-esteem and physical self-worth are fractal, resulting from individuals' coupling to everyday social and environmental events.
• The fractal dynamics of self-esteem and physical self have been studied by Delignières, Fortes, and Ninot (2004).