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Visualization of nonlocality in coupled map latices

Janowicz M., Kaleta J., Wrzeciono P., Zembrzuski A., Orłowski A.

Machine Graphics and Vision

2016

Vol. 25, No. 1/4

13--25

Numerical simulations of coupled map lattices with various degree of nonlocality have been performed. Quantitative characteristics of recently introduced for local coupling have been applied in the nonlocal case. It has been attempted to draw qualitative conclusions about nonlocality from the emerging pictures.

Efficiency analysis of control algorithms in spatially distributed systems with chaotic behavior

Korus Ł.

International Journal of Applied Mathematics and Computer Science

2014

Vol. 24, no. 4

759--770

The paper presents results of examination of control algorithms for the purpose of controlling chaos in spatially distributed systems like the coupled map lattice (CML). The mathematical definition of the CML, stability analysis as well as some basic results of numerical simulation exposing complex, spatiotemporal and chaotic behavior of the CML were already presented in another paper. The main purpose of this article is to compare the efficiency of controlling chaos by simple classical algorithms in spatially distributed systems like CMLs. This comparison is made based on qualitative and quantitative evaluation methods proposed in the previous paper such as the indirect Lyapunov method, Lyapunov exponents and the net direction phase indicator. As a summary of this paper, some conclusions which can be useful for creating a more efficient algorithm of controlling chaos in spatially distributed systems are made.

Simple environment for developing methods of controlling chaos in spatially distributed systems

Korus Ł.

International Journal of Applied Mathematics and Computer Science

2011

Vol. 21, no 1

149-159

The paper presents a simple mathematical model called a coupled map lattice (CML). For some range of its parameters, this model generates complex, spatiotemporal behavior which seems to be chaotic. The main purpose of the paper is to provide results of stability analysis and compare them with those obtained from numerical simulation. The indirect Lyapunov method and Lyapunov exponents are used to examine the dependence on initial conditions. The net direction phase is introduced to measure the symmetry of the system state trajectory. In addition, a real system, which can be modeled by the CML, is presented. In general, this article describes basic elements of environment, which can be used for creating and examining methods of chaos controlling in systems with spatiotemporal dynamics.