| Abstract: |
In this thesis, modifications and extensions of cell mapping (CM) methodsare presented. CM methods are tools for the global investigation of the longterm behaviour of nonlinear dynamic systems. By means of CM, periodicas well as chaotic solutions of the equations of motion can be determined.Additionally, application of CM enables the determination of the basins ofattraction of the stable solutions.First, an overview is given of existing CM methods. The simple cellmapping (SCM) method is based on a discretization of the state space incells, followed by a determination-by means of numerical integration-ofcorresponding image cells. Groups of periodic cells represent the system’slong term behaviour. The generalized cell mapping (GCM) method is a gen-eralization of SCM. Because of the probabilistic approach involved, GCMis particularly suited for the description of chaotic behaviour. Under in-terpolated cell mapping (ICM), approximations of state space trajectoriesare created by means of interpolation. Finally, multiple mapping (MM) isa modification to ICM, yielding more accurate results in case of high statespace distortions.Next, some modifications are presented which increase the accuracy andefficiency of the existing CM methods. For autonomous systems, a dimen-sion reduction method is given. Subsequently, modifications are given whichare necessary to make cell mapping methods applicable to discontinuoussystems. For ICM, a modification is introduced which speeds up the in-terpolation process. Further, a combination of ICM and MM is discussed,termed mixed cell mapping (MCM). Finally, the advantages are shown ofusing an extended integration interval under SCM.In addition to these modifications, two substantial extensions of the ex-isting CM methods are presented. The first extension contains a parametervariation technique, suited for the sensitivity-analysis of CM results with re-spect to system parameters. With this technique, the evolution of the basinboundaries due to a parameter variation can be obtained in relatively littlexCPU-time. In thi~introduced conceptThe second extping (MDCM), wdom. Since the nrequirements-grocation of conventioUnder MDCM, thesi on while the order]For illustrationtwo practical nonlinrotor with rubbing !,attraction of a coexirespond to a motioof a portable CD pIthe player to a perioconditions.It is concludedmerit. Further, therespect to more estaband regular numericalthe investigation of nof CM methods.
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