Period-doubled spiral waves without line defects in oscillatory systems

Spiral waves are common self-organized spatiotemporal patterns in nature and experimental systems, playing a particularly crucial role in cardiac tissues and neuronal networks. Traditional spiral waves in period-2 domains typically exhibit defect lines, which can significantly influence spiral wave dynamics and have attracted considerable attention in recent years. The regulation of line defects in spiral waves holds significant implications in various domains, including cardiology and neuroscience. Here, we utilize periodic forcing to eliminate line defects in the traditional period-doubled spiral waves, resulting in a different form of the period-doubled spiral wave, named the restless spiral wave. The disappearance of line defects restores spiral waves to a simple helical structure but does not reinstate their rotational symmetry. The waves in the restless spiral wave are coherent at a certain moment but exhibit periodic oscillations during propagation. Analysis indicates that the disappearance of line defects occurs at the expense of the breaking of symmetry in the distribution of local point states in phase space. This method overcomes the limitations of traditional defect line-dependent control strategies, providing a different approach to controlling arrhythmias in cardiac tissue and studying wave dynamics in neuroscience.