Suppression of spiral wave turbulence by means of periodic plane waves in two-layer excitable media

2019 ◽  
Vol 128 ◽  
pp. 229-233 ◽  
Author(s):  
Zhen Wang ◽  
Zahra Rostami ◽  
Sajad Jafari ◽  
Fawaz E. Alsaadi ◽  
Mitja Slavinec ◽  
...  
2021 ◽  
Vol 31 (5) ◽  
pp. 053131
Author(s):  
Karthikeyan Rajagopal ◽  
Shaobo He ◽  
Anitha Karthikeyan ◽  
Prakash Duraisamy

1993 ◽  
Vol 03 (05) ◽  
pp. 1269-1279 ◽  
Author(s):  
JONATHAN A. SHERRATT

Transition waves are widespread in the biological and chemical sciences, and have often been successfully modelled using reaction–diffusion systems. I consider a particular system of three reaction–diffusion equations, and I show that transition waves can destabilise as the kinetic ordinary differential equations pass through a Hopf bifurcation, giving rise to either regular or irregular spatiotemporal oscillations behind the advancing transition wave front. In the case of regular oscillations, I show that these are periodic plane waves that are induced by the way in which the transition wave front approaches its terminal steady state. Further, I show that irregular oscillations arise when these periodic plane waves are unstable as reaction–diffusion solutions. The resulting behavior is not related to any chaos in the kinetic ordinary differential equations.


1996 ◽  
Vol 77 (15) ◽  
pp. 3244-3247 ◽  
Author(s):  
Takashi Amemiya ◽  
Sándor Kádár ◽  
Petteri Kettunen ◽  
Kenneth Showalter

Author(s):  
Vladimir Zykov ◽  
Eberhard Bodenschatz

Abstract Spiral waves are a well-known and intensively studied dynamic phenomenon in excitable media of various types. Most studies have considered an excitable medium with a single stable resting state. However, spiral waves can be maintained in an excitable medium with bistability. Our calculations, performed using the widely used Barkley model, clearly show that spiral waves in the bistability region exhibit unique properties. For example, a spiral wave can either rotate around a core that is in an unexcited state, or the tip of the spiral wave describes a circular trajectory located inside an excited region. The boundaries of the parameter regions with positive and "negative" cores have been defined numerically and analytically evaluated. It is also shown that the creation of a positive or "negative" core may depend on the initial conditions, which leads to hysteresis of spiral waves. In addition, the influence of gradient flow on the dynamics of the spiral wave, which is related to the tension of the scroll wave filaments in a three-dimensional medium, is studied.


eLife ◽  
2018 ◽  
Vol 7 ◽  
Author(s):  
Rupamanjari Majumder ◽  
Iolanda Feola ◽  
Alexander S Teplenin ◽  
Antoine AF de Vries ◽  
Alexander V Panfilov ◽  
...  

Propagation of non-linear waves is key to the functioning of diverse biological systems. Such waves can organize into spirals, rotating around a core, whose properties determine the overall wave dynamics. Theoretically, manipulation of a spiral wave core should lead to full spatiotemporal control over its dynamics. However, this theory lacks supportive evidence (even at a conceptual level), making it thus a long-standing hypothesis. Here, we propose a new phenomenological concept that involves artificially dragging spiral waves by their cores, to prove the aforementioned hypothesis in silico, with subsequent in vitro validation in optogenetically modified monolayers of rat atrial cardiomyocytes. We thereby connect previously established, but unrelated concepts of spiral wave attraction, anchoring and unpinning to demonstrate that core manipulation, through controlled displacement of heterogeneities in excitable media, allows forced movement of spiral waves along pre-defined trajectories. Consequently, we impose real-time spatiotemporal control over spiral wave dynamics in a biological system.


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