The concept of feedback-anticipative control as the extension of classical Wiener paradigm is considered in the context of multi agent systems. The behavior of
complex real world agents is based on the consideration of feedback information as well as on the anticipation. A linear model
of the agents with a nonlinear interaction rule is proposed as the mean for the methodological conception. The results of
the developed system display a periodic response. An analytical determination of periodicity conditions for individual agents
was performed by the application of z-transform. Proof of system stability for the case of two interacting agents has been provided. The hyperincursivity paradigm is presented
as an interesting methodological platform for further investigation of multi agent systems.
[Show abstract][Hide abstract] ABSTRACT: This paper deals with a simple multiplier-accelerator model of the business cycle, including a cubic nonlinearity. The corresponding two dimensional iterative map is represented in terms of its bifurcation diagram in parameter space. A number of bifurcation sequences for attractors and their basins are studied.
[Show abstract][Hide abstract] ABSTRACT: Many natural and human-made nonlinear oscillators exhibit the ability to adjust their rhythms due to weak interaction: two lasers, being coupled, start to generate with a common frequency; cardiac pacemaker cells fire simultaneously; violinists in an orchestra play in unison. Such coordination of rhythms is a manifestation of a fundamental nonlinear phenomenon--synchronization. Discovered in the 17th century by Christiaan Huygens, it was observed in physics, chemistry, biology and even social behaviour, and found practical applications in engineering and medicine. The notion of synchronization has been recently extended to cover the adjustment of rhythms in chaotic systems, large ensembles of oscillating units, rotating objects, continuous media, etc. In spite of essential progress in theoretical and experimental studies, synchronization remains a challenging problem of nonlinear sciences.
[Show abstract][Hide abstract] ABSTRACT: The model of interacting anticipative Kaldor's cobweb agents, where emergence of stabilizing behavior could be observed, is determined by the sets of difference equations and discrete rules. A general interaction rule between the agents is determined by the floor-roof principle. The agents' synchronization is the main property of the system response. The synchronization rule was determined by an application of z-transform. A nonlinear expansion of the anticipative model provided attractor response. A determination of stability is explored by the regions where Lyapunov exponents are negative. An analytical determination of stability region is proposed.
WSEAS Transactions on Mathematics 12/2006; 5(12):1282-1289.
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