SPATIOTEMPORAL DYNAMICS OF COUPLED ARRAY OF MURALI–LAKSHMANAN–CHUA CIRCUITS
SPATIOTEMPORAL DYNAMICS OF COUPLED ARRAY OF MURALI–LAKSHMANAN–CHUA CIRCUITS
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DOI：
10.1142/s0218127499000572
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发表时间：
1997-08
影响因子：
2.2
通讯作者：
Paulsamy Muruganandam;K. Murali;M. Lakshmanan
中科院分区：
文献类型：
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作者：
Paulsamy Muruganandam;K. Murali;M. Lakshmanan
最近由Murali，Lakshmanan和Chua提出的电路（MLC）是最简单的非自治非线性电路之一，它表现出包括各种分岔、混沌等在内的多种动力学现象.本文研究了在无周期外力和有周期外力作用下，耦合MLC电路的一维和二维阵列的时空动力学.在没有外力作用的情况下，通过数值模拟观察到行波波前的传播现象及其失效。我们已经表明，传播的波前是由于稳定状态（固定前）的稳定性的损失，通过亚临界分岔耦合的存在下的necessary盆地的吸引力的稳定状态。我们还研究了弱耦合对一维阵列中由于稳定波前的存在而导致波前阻塞的传播现象的影响。此外，我们已经观察到的自发形成的六边形图案（五-七缺陷）由于图灵不稳定性的二维阵列。我们表明，从六方到菱形结构的过渡发生的外部周期性力的影响。我们还显示了过渡从六边形卷和六边形呼吸（时空周期振荡）运动中存在的外部周期力。我们进一步分析了耦合MLC电路（在一维）的时空混沌动力学的影响下，外部周期强迫。在这里，我们注意到，动态是严重依赖于系统的大小。在阈值尺寸以上，时空混沌的抑制发生，导致时空规则（周期性）图案，即使单个MLC电路本身显示出混沌行为。然而，低于这个临界尺寸，时空混沌的同步观察。
The circuit recently proposed by Murali, Lakshmanan and Chua (MLC) is one of the simplest nonautonomous nonlinear electronic circuits which show a variety of dynamical phenomena including various bifurcations, chaos and so on. In this paper we study the spatiotemporal dynamics in one- and two-dimensional arrays of coupled MLC circuits both in the absence as well as in the presence of external periodic forces. In the absence of any external force, the propagation phenomena of traveling wavefront and its failure have been observed from numerical simulations. We have shown that the propagation of the traveling wavefront is due to the loss of stability of the steady states (stationary front) via subcritical bifurcation coupled with the presence of neccessary basin of attraction of the steady states. We also study the effect of weak coupling on the propagation phenomenon in one-dimensional array which results in the blocking of wavefront due to the existence of a stationary front. Further we have observed the spontaneous formation of hexagonal patterns (with penta–hepta defects) due to Turing instability in the two-dimensional array. We show that a transition from hexagonal to rhombic structures occur by the influence of an external periodic force. We also show the transition from hexagons to rolls and hexagons to breathing (space-time periodic oscillations) motion in the presence of external periodic force. We further analyze the spatiotemporal chaotic dynamics of the coupled MLC circuits (in one dimension) under the influence of external periodic forcing. Here we note that the dynamics is critically dependent on the system size. Above a threshold size, a suppression of spatiotemporal chaos occurs, leading to a space-time regular (periodic) pattern eventhough the single MLC circuit itself shows a chaotic behavior. Below this critical size, however, a synchronization of spatiotemporal chaos is observed.