Arkady Zgonnikov
ABSTRACT
We analyze data collected during the series of experiments aimed at elucidation of basic properties of human perception, namely, the limited capacity of ordering events, actions, etc. according to their preference. Previously it was shown that in a wide class of human-controlled systems small deviations from the equilibrium position do not cause any actions of the system's operator, so any point in a certain neighborhood of equilibrium position is treated as an equilibrium one. This phenomenon can be described by the notion of dynamical traps that was introduced to denote a region in the system phase space where the object under consideration cannot clearly determine the most preferable of the positions that are similar in some sense. According to this concept, the motion of the system in the dynamical trap region is mainly not affected by the operator. The moments of time when the system leaves the dynamical trap region, or in other words, when the operator decides to start or stop the control over the system, are called action points [1]. These moments are seem to be determined intuitively by the operator, and the purpose of our work is to understand the nature of such intuitive decision making process by investigating the action points data obtained from the experiments.
- Todosiev, E. P., The action point model of the driver-vehicle system, Techical Report 202A-3 (Ph.D. thesis), Ohio State University, 1963.Google Scholar
- Chakrabarti, B. K., Chakraborti, A., and Chatterjee, A. (eds.) Econophysics and Sociophysics: Trends and Perspectives, (Wiley VCH Verlag, Weinheim, 2006).Google Scholar
- Galam, S., Sociophysics: A review of Galam models, Int. J. Mod. Phys. 19 (2008) 409--440.Google ScholarCross Ref
- Castellano, C., Fortunato, S., and Loreto, V. Statistical physics of social dynamics, Rev. Mod. Phys. 81 (2009) 591--646.Google ScholarCross Ref
- Nowak, A, and Strawinska, U., Applications of Physics and Mathematics to Social Science, Introduction to, in Encyclopedia of Complexity and Systems Science, ed. Meyers, R. A. (2009 SpringerScience+Business Media, LLC., New York, 2009), pp. 322--326.Google Scholar
- Slanina, F., Social Processes, Physical Models of, in ibid. pp. 8379--8405.Google Scholar
- Helbing, D. and Johansson, A., Pedestrian, Crowd and Evacuation Dynamics, in ibid., pp. 6476--6495.Google Scholar
- Lubashevsky, I. A., Mahnke, R., Hajimahmoodzadeh, M., and Katsnelson, A., Long-lived states of oscillator chains with dynamical traps, Eur. Phys. J. B 44 (2005) 63--70.Google ScholarCross Ref
- Lubashevsky, I, Hajimahmoodzadeh, M., Katsnelson, A., and Wagner, P., Noise-induced phase transition in an oscillatory system with dynamical traps, Eur. Phys. J. B 36 (2003) 115--118.Google ScholarCross Ref
- Lubashevsky, I. A., Gafiychuk, V. V., and Demchuk, A. V., Anomalous relaxation oscillations due to dynamical traps, Physica A 255 (1998) 406--414.Google ScholarCross Ref
- Lubashevsky, I., Mahnke, R., Wagner, P., Kalenkov, S., Long-lived states in synchronized traffic flow: Empirical prompt and dynamical trap model, Phys. Rev. E 66 (2002) 016117.Google ScholarCross Ref
- Zaslavsky, G. M., Hamiltonian Chaos and Fractional Dynamics (Oxford University Press, 2005).Google Scholar
Index Terms
- Computer simulation of stick balancing: action point analysis
Recommendations
Dynamics in spectral solutions of Burgers equation
For low values of the viscosity coefficient, Burgers equation can develop sharp discontinuities, which are difficult to simulate in a computer. Oscillations can occur by discretization through spectral collocation methods, due to Gibbs phenomena. Under ...
Application of a new theory of fuzzy chaos for the simulation and control of nonlinear dynamical systems
We describe in this article a new theory of chaos using fuzzy logic techniques. Chaotic behavior in nonlinear dynamical systems is very difficult to detect and control. Part of the problem is that mathematical results for chaos are difficult to use in ...
Bifurcations and chaos in passive dynamic walking
Irrespective of achieving certain success in comprehending Passive Dynamic Walking (PDW) phenomena from a viewpoint of the chaotic dynamics and bifurcation scenarios, a lot of questions still need to be answered. This paper provides an overview of the ...
Comments