scholarly journals A Switching Hybrid Dynamical System: Toward Understanding Complex Interpersonal Behavior

2018 ◽  
Vol 9 (1) ◽  
pp. 39
Author(s):  
Yuji Yamamoto ◽  
Akifumi Kijima ◽  
Motoki Okumura ◽  
Keiko Yokoyama ◽  
Kazutoshi Gohara
Keyword(s):  
Dynamical System ◽  
Phase Synchronization ◽  
Transition Probabilities ◽  
Discrete Dynamical System ◽  
Interpersonal Behavior ◽  
Switching Behavior ◽  
System Perspective ◽  
Hybrid Dynamics ◽  
Switching Dynamics ◽  
Coordination Patterns

Complex human behavior, including interlimb and interpersonal coordination, has been studied from a dynamical system perspective. We review the applications of a dynamical system approach to a sporting activity, which includes continuous, discrete, and switching dynamics. Continuous dynamics identified switching between in- and anti-phase synchronization, controlled by an interpersonal distance of 0.1 m during expert kendo matches, using a relative phase analysis. In the discrete dynamical system, return map analysis was applied to the time series of movements during kendo matches. Offensive and defensive maneuvers were classified as six coordination patterns, that is, attractors and repellers. Furthermore, these attractors and repellers exhibited two discrete states. Then, state transition probabilities were calculated based on the two states, which clarified the coordination patterns and switching behavior. We introduced switching dynamics with temporal inputs to clarify the simple rules underlying the complex behavior corresponding to switching inputs in a striking action as a non-autonomous system. As a result, we determined that the time evolution of the striking action was characterized as fractal-like movement patterns generated by a simple Cantor set rule with rotation. Finally, we propose a switching hybrid dynamics to understand both court-net sports, as strongly coupled interpersonal competition, and weakly coupled sports, such as martial arts.

scholarly journals A Switching Hybrid Dynamical System: Toward Understanding Complex Interpersonal Behavior

2018 ◽  
Author(s):  
Yuji Yamamoto ◽  
Akifumi Kijima ◽  
Motoki Okumura ◽  
Keiko Yokoyama ◽  
Kazutoshi Gohara
Keyword(s):  
Dynamical System ◽  
Phase Synchronization ◽  
Transition Probabilities ◽  
Interpersonal Behavior ◽  
Switching Behavior ◽  
System Perspective ◽  
Strongly Coupled ◽  
Hybrid Dynamics ◽  
Switching Dynamics ◽  
Coordination Patterns

Complex human behavior, including interlimb and interpersonal coordination, has been studied from a dynamical system perspective. We review the applications of a dynamical system approach to a sporting activity, which includes continuous, discrete, and switching dynamics. Continuous dynamics identified switching between in- and anti-phase synchronization, controlled by an interpersonal distance of 0.1 m during expert kendo matches, using a relative phase analysis. As discrete dynamics, return map analysis was applied to the time series of movements during kendo matches, and six coordination patterns were classified. Furthermore, state transition probabilities were calculated based on the two states, which clarified the coordination patterns and switching behavior. We introduced switching dynamics with temporal inputs to clarify the simple rules underlying the complex behavior corresponding to switching inputs in a striking action as a non-autonomous system. As a result, we determined that the time evolution of the striking action was characterized as fractal-like movement patterns generated by a simple Cantor set rule with rotation. Finally, we propose a switching hybrid dynamics to understand both court-net sports, as strongly coupled interpersonal competition, and weakly coupled sports, such as martial arts.

scholarly journals Potential Well in Poincaré Recurrence

Entropy ◽  
2021 ◽  
Vol 23 (3) ◽  
pp. 379
Author(s):  
Miguel Abadi ◽  
Vitor Amorim ◽  
Sandro Gallo
Keyword(s):  
Dynamical System ◽  
Dynamical Systems ◽  
Stochastic Processes ◽  
Recurrence Time ◽  
Potential Well ◽  
Exponential Approximation ◽  
Mixing Processes ◽  
System Perspective ◽  
Return Times ◽  
Error Terms

From a physical/dynamical system perspective, the potential well represents the proportional mass of points that escape the neighbourhood of a given point. In the last 20 years, several works have shown the importance of this quantity to obtain precise approximations for several recurrence time distributions in mixing stochastic processes and dynamical systems. Besides providing a review of the different scaling factors used in the literature in recurrence times, the present work contributes two new results: (1) For ϕ-mixing and ψ-mixing processes, we give a new exponential approximation for hitting and return times using the potential well as the scaling parameter. The error terms are explicit and sharp. (2) We analyse the uniform positivity of the potential well. Our results apply to processes on countable alphabets and do not assume a complete grammar.

Towards a More Holistic Approach to Quality Improvements in Aluminium Die Casting

2009 ◽  
Vol 618-619 ◽  
pp. 341-344
Author(s):  
Sandrine Zanna ◽  
Yakov Frayman ◽  
Bruce Gunn ◽  
Saeid Nahavandi
Keyword(s):  
Dynamical System ◽  
System Theory ◽  
Die Casting ◽  
Holistic Approach ◽  
Natural Process ◽  
Dynamical System Theory ◽  
Quality Improvements ◽  
System Perspective ◽  
Porosity Defects ◽  
Natural Equilibrium

This work evaluates the feasibility of using a holistic approach, based on dynamical system theory, to reduce porosity defects in high pressure aluminum die casting. Quality improvements, from a dynamical system perspective mean the ability to move the die casting process out of its natural equilibrium to a more beneficial state and the ability to maintain this new process state. This more beneficial state may be achieved in several ways. One way is to increase the amount of forcing to overcome natural process resistance. This forcing approach is represented by typical continuous intervention policy, with modifications in die/part design and/or process parameters. An alternative approach is to reduce the amount of natural process resistance, in particular the amount of process disturbance, allowing the process to move out of its natural equilibrium with much less forcing. This alternative uses the self-regulating ability of dynamical systems thus decreasing the amount of human intervention required. In this respect, the influence of vacuum on time on chattering at the first stage of the casting shot was identified as a good process candidate for testing using dynamical system theory. A significant reduction in porosity defects was achieved, which also set the process on a path of slow but consistent self-improvement.

Identification of gene interactions in fungal–plant symbiosis through discrete dynamical system modelling

2009 ◽  
Vol 3 (5) ◽  
pp. 414-428 ◽  
Author(s):  
J.G.C. Angeles ◽  
Z. Ouyang ◽  
A.M. Aguirre ◽  
P.J. Lammers ◽  
M. Song
Keyword(s):  
Dynamical System ◽  
Discrete Dynamical System ◽  
Gene Interactions ◽  
System Modelling

scholarly journals Cosmological dynamics of brane gravity: A global dynamical system perspective

2018 ◽  
Vol 98 (8) ◽  
Author(s):  
Hmar Zonunmawia ◽  
Wompherdeiki Khyllep ◽  
Jibitesh Dutta ◽  
Laur Järv
Keyword(s):  
Dynamical System ◽  
System Perspective ◽  
Brane Gravity

scholarly journals $(q,t)$-Characters of Kirillov-Reshetikhin Modules of Type $A_r$ as Quantum Cluster Variables

10.37236/7188 ◽  
2018 ◽  
Vol 25 (1) ◽  
Author(s):  
Bolor Turmunkh
Keyword(s):  
Dynamical System ◽  
Discrete Dynamical System ◽  
Cluster Algebra ◽  
Quiver Varieties ◽  
Quantum Cluster ◽  
T System

Nakajima (2003) introduced a $t$-deformation of $q$-characters, $(q,t)$-characters for short, and their twisted multiplication through the geometry of quiver varieties. The Nakajima $(q,t)$-characters of Kirillov-Reshetikhin modules satisfy a $t$-deformed $T$-system. The $T$-system is a discrete dynamical system that can be interpreted as a mutation relation in a cluster algebra in two different ways, depending on the choice of direction of evolution. In this paper, we show that the Nakajima $t$-deformed $T$-system of type $A_r$ forms a quantum mutation relation in a quantization of exactly one of the cluster algebra structures attached to the $T$-system.

Geometry and Kinematics of Cylindrical Waterbomb Tessellation

2021 ◽  
Author(s):  
Rinki Imada ◽  
Tomohiro Tachi
Keyword(s):  
Dynamical System ◽  
Recurrence Relation ◽  
Discrete Dynamical System ◽  
Kinematic Model ◽  
Theoretical Reason ◽  
Finite Solution ◽  
Geometry And Kinematics ◽  
Folded Surfaces

Abstract Folded surfaces of origami tessellations have attracted much attention because they sometimes exhibit non-trivial behaviors. It is known that cylindrical folded surfaces of waterbomb tessellation called waterbomb tube can transform into wave-like surfaces, which is a unique phenomenon not observed on other tessellations. However, the theoretical reason why wave-like surfaces arise has been unclear. In this paper, we provide a kinematic model of waterbomb tube by parameterizing the geometry of a module of waterbomb tessellation and derive a recurrence relation between the modules. Through the visualization of the configurations of waterbomb tubes under the proposed kinematic model, we classify solutions into three classes: cylinder solution, wave-like solution, and finite solution. Furthermore, we give proof of the existence of a wave-like solution around one of the cylinder solutions by applying the knowledge of the discrete dynamical system to the recurrence relation.

scholarly journals The Limit Point of the Pentagram Map

2018 ◽  
Vol 2020 (9) ◽  
pp. 2818-2831 ◽  
Author(s):  
Max Glick
Keyword(s):  
Dynamical System ◽  
Limit Point ◽  
Convex Polygon ◽  
Discrete Dynamical System ◽  
Explicit Description ◽  
Cartesian Coordinates ◽  
The Subject ◽  
Pentagram Map

Abstract The pentagram map is a discrete dynamical system defined on the space of polygons in the plane. In the 1st paper on the subject, Schwartz proved that the pentagram map produces from each convex polygon a sequence of successively smaller polygons that converges exponentially to a point. We investigate the limit point itself, giving an explicit description of its Cartesian coordinates as roots of certain degree three polynomials.

Sign in / Sign up

Export Citation Format

Share Document