Journal Article

On the Formation of Particlelike Patterns, the Amplitude Modulated Route to Chaos and the Wave-Particle Dualism in Three-Dimensional Dynamic Systems under Global Constraints

G. Sonnemann

in Progress of Theoretical Physics

Published on behalf of The Physical Society of Japan

Volume 99, issue 6, pages 931-962
Published in print June 1998 | ISSN: 0033-068X
Published online June 1998 | e-ISSN: 1347-4081 | DOI: https://dx.doi.org/10.1143/PTP.99.931
On the Formation of Particlelike Patterns, the Amplitude Modulated Route to Chaos and the Wave-Particle Dualism in Three-Dimensional Dynamic Systems under Global Constraints

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Spatiotemporally stable solutions have been found for nonlinear partial integro-differential equation systems including diffusion. These mathematical systems were originally derived from an immunological problem of the modelling of an inflammation process. An extended system is able to form quasi-stable particles marked by a characteristic internal structure and dynamics of this structure. Properties of such particles are investigated by employing a selected set of system parameters. The system driving parameter is chosen as a control parameter. Increasing this parameter steadily, the system crosses some bifurcation points connected with a catastrophic change of state of the particle. The particle finally becomes chaotic. A new route to chaos occurs on this occasion. The particle emits a weak space wave. Different outcomes of the model runs are discussed.

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