Schneider Felix M, Schöll Eckehard, Dahlem Markus A
Institut fur Theoretische Physik, Technische Universitat Berlin, Berlin, Germany.
Chaos. 2009 Mar;19(1):015110. doi: 10.1063/1.3096411.
The onset of pulse propagation is studied in a reaction-diffusion (RD) model with control by augmented transmission capability that is provided either along nonlocal spatial coupling or by time-delayed feedback. We show that traveling pulses occur primarily as solutions to the RD equations, while augmented transmission changes excitability. For certain ranges of the parameter settings, defined as weak susceptibility and moderate control, respectively, the hybrid model can be mapped to the original RD model. This results in an effective change in RD parameters controlled by augmented transmission. Outside moderate control parameter settings new patterns are obtained, for example, stepwise propagation due to delay-induced oscillations. Augmented transmission constitutes a signaling system complementary to the classical RD mechanism of pattern formation. Our hybrid model combines the two major signaling systems in the brain, namely, volume transmission and synaptic transmission. Our results provide insights into the spread and control of pathological pulses in the brain.
在一个反应扩散（RD）模型中研究了脉冲传播的起始，该模型通过增强传输能力进行控制，增强传输能力可通过非局部空间耦合或延迟反馈来实现。我们表明，行波脉冲主要作为RD方程的解出现，而增强传输会改变兴奋性。对于分别定义为弱敏感性和适度控制的某些参数设置范围，混合模型可以映射到原始的RD模型。这导致由增强传输控制的RD参数发生有效变化。在适度控制参数设置范围之外，会获得新的模式，例如，由于延迟诱导振荡导致的逐步传播。增强传输构成了一种与经典的RD模式形成机制互补的信号系统。我们的混合模型结合了大脑中的两个主要信号系统，即容积传输和突触传输。我们的结果为大脑中病理性脉冲的传播和控制提供了见解。
