On holonomic mathematical F - pendulum

• Published in: Mathematical methods in the applied sciences Vol. 39; no. 16; pp. 4820 - 4828
• Main Authors: Buslaev, Alexander P., Yashina, Marina V.
• Format: Journal Article
• Language: English
• Published: Freiburg Blackwell Publishing Ltd 15-11-2016; Wiley Subscription Services, Inc
• Subjects: Chaos theory; competition rules; dynamical system; Dynamical systems; Graphs; logistical plan; Logistics; Mathematical models; Pendulums; Phase shift; real-value pendulums; synchronization of parallel processes; transportation-logistics problem
• ISSN: 0170-4214; 1099-1476
• DOI: 10.1002/mma.3810

A discrete dynamical system named real ‐ valued pendulum is presented in the paper. The system is developed for modeling of particles relocations on graph with formalized rules of behavior (competition for space) and movement plans logistics. Logistics is given in a formal statement by the real numbers of the unit closed interval, presented in calculus with base equals to the graph power N.
The central question is to study the behavior of the pendulum depending on its architecture.
In the previous papers, with investigation of logistic pendulum, we have studied chaotic pendulum, where the particle plan for “tomorrow” is played “today”. A particular case of logistic pendulum, such that particle plans are time shifts of N−ary digital representation of single generating number, is called phase pendulum.
In this paper, we are considering a dynamical system with generation of particles plans using a some mapping F, defined on the set of system states. Copyright © 2016 John Wiley & Sons, Ltd.