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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.

Simple model of spatiotemporal chaos nucleate boiling

Mosdorf R.

Zeszyty Naukowe Politechniki Świętokrzyskiej. Mechanika

1999

Z. 67

293--302

The model presented in the paper simulates the changes of the heating surface temperature under 80 nucleate sites. Process of bubble generation has been modelled by changing of boundary condition on the heating surface. Results of simulation show that when the rate of heat flux absorbed by vapour bubble exceeds a critical rate the phenomenon of spatiotemporal chaos is observed. Calculations of largest Lyapunov exponent show that changes of heating surface temperature have deterministic chaos character. Calculations of correlation dimension show that an atractor created by subsequent values of heating surface temperature has correlation dimension equal to D2≈3,5.