Defect development in a three-dimensional reaction-diffusion system with gradient

The formation and development of spiral defects is one of the major causes of order-disorder transitions in spatiotemporal patterns. In this paper, line defect formation and development in a three-dimensional reaction-diffusion system with gradients of control parameters in the third dimension is investigated. The system can be considered as diffusively coupled two-dimensional spatiotemporal patterns with dissimilarities. We observed that under certain conditions, as the gradients are varied, ordered and disordered spatiotemporal patterns appear alternately and line defects of various configurations form. This scenario is found to be in qualitative agreement with the experimental findings in the Belousov-Zhabotinsky reaction. We thus demonstrate that the line defect which was usually expected in two-dimensional complex oscillatory media can also be generated from the reconciliation between the coupled simple spiral waves with dissimilarity.