本科毕业设计（论文）
外文翻译
Quorum Sensing in Populations of Spatially Extended Chaotic Oscillators Coupled Indirectly via a Heterogeneous Environment
出处：J. Nonlinear. Sci.
- Introduction
Synchronization, firstly discovered by Huygens at least 300 years ago, has been recognized as a universal concept in the realm of nonlinear science. The synchronized motion is of fundamental importance in coordinating the rhythmic behavior among individuals in various systems from physics, chemistry to biology. Well-known examples include the arrays of lasers Josephson junction series, assembles of chemical oscillators, cardiac muscle cells and neurons in brain. In cardiovascular science, synchronous contraction of the heart is essential to pump blood throughout the whole body, while asynchronous contraction of the heart may lead to serious cardiac arrhythmias. In neuroscience, synchronization is believed to be a central mechanism for neuronal information processing within a brain area and also for communication between different areas of the brain. The synchronized oscillation, on the other hand, could also lead to several neurological diseases such as epileptic seizures and Parkinsonrsquo;s disease.
To investigate the synchronization behaviors in complex systems, a popular and an efficient approach is treating the systems as ensembles of oscillators that are coupled in a direct manner. However, in many systems such as bacteria, yeast cells and social amoebae Dictyostelium discoideum, the synchronized oscillation is believed to arise through communication by chemical signaling molecules via the extracellular solution. The elements in these systems are not influenced by each other in a direct fashion, but rather indirectly through a common environment. A common finding for these systems is that the density of population plays a vital role in determining the dynamical state of the system. For instance, a typical scenario is that as the population density of the element increases and exceeds some threshold value, the system suddenly switches from the quiescent state to the state of synchronized oscillation for all the elements. Such a transition is typically referred to as dynamical “quorum sensing”(QS). The dynamical QS transition has also been reported in nonliving systems like a large population of indirectly coupled chemical oscillators and lasers.
Originally, QS was interpreted simply as a means for bacteria to coordinate the collective cellular behaviors within physically and chemically homogeneous cultures. Therefore, in general, QS research focused on the well-stirred systems, i.e., they assumed that the concentration of the signaling molecules was distributed uniformly in the external environment. In other words, each element of the system fell the same dynamical environment. But it is now recognized that QS essentially occurs in a complex environment that may be physically, chemically and biologically heterogeneous and under such a condition signaling molecules are transported primarily by the local diffusion. The interaction between the reaction and local diffusion can lead to the emergence of the more complex spatiotemporal patterns compared to the case of homogeneous environment.
With systematic investigations, various dynamical synchronization states [e.g., oscillation death (OD), phase synchronization (PS), and complete synchronization oscillation (CSO)] and their corresponding transitions were observed. In particular, a non-traditional quorum sensing transition was uncovered: increasing the density would first lead to collective oscillation from oscillation quench, but further increasing the population density would lead to decrease of degree of synchronization. Specifically, for the small size system, the degeneration of CSO to PS was observed, and for large population the transition from PS to desynchronization occurred. We attributed these new finding to the dual roles played by the population density. Whatrsquo;s more, the full system was effectively equivalent to a locally coupled system if one treated the environment as another component of the oscillator. This fact allowed us to analyze the occurrence of CSO based on the master stability functions (MSF) approach. The result from the MSF calculation was in agreement with that from the direct numerical integration of the system.
2. The Model and Numerical Method
2.1 A General Model
As irregular or even chaotic oscillation is ubiquitously observed and it reflects the realistic situations in natural or engineered systems (e.g., the oscillation of the bulk fluorescence is irregular in genetic regulation network used in Danino et al. 2010).
(1)
(2)
In Eq.(3),the parameter represents the intrinsic frequency of the th oscillator. For the sake of simplicity, all the oscillators are supposed to be identical and we set . With , the isolated oscillator (i.e., ) shows chaotic oscillation.
Previous works on directly coupled chaotic oscillators have shown that their collective dynamics much more complicated and offered even richer phenomena. In comparison with directly coupled chaotic oscillators, the works on collective behavior of indirectly coupled oscillators has been m
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