Research area

Research at Centre for Nonlinear Studies

The research at the Centre for Nonlinear Studies has covered several directions in nonlinear science, such as statistical physics, condensed matter physics, biophysics, and nonlinear optics. Our current research focus is on analysis and modeling of dynamical processes of complex systems.

Complex systems are everywhere, ranging from physics, life science to human society. Recently, due to the development of experimental and information technologies, there is an rapid accumulation of massive data for biological and social systems. It has been shown that most real complex systems are characterized by complex networked interaction and highly fluctuating dynamical activity. Complexity research now calls for new methodologies to obtain a more quantitative understanding of various complex systems by integrating the approaches of theoretical modeling and computer simulations with experimental or empirical data.

Our work emphasizes understanding the structure-dynamics-function relationship in complex network systems by studying the impact of complex network topology on various dynamical processes, such as synchronization of oscillators, avalanches of neural firing, and individual and collective human dynamics.

One important research direction of the Centre is analysis and modeling of complex network structure and activity in neural systems. We carry out research in close collaboration with neuroscientists, using the approaches of oscillatory dynamical networks and covering broad scales from network of neurons to interacting functional brain regions and cognitive performance.

The research activity includes but not limited to the following topics:

1)Complex neural networks and structure-function relationship
2)Self-organized activity and information processing in complex neural networks
3)Complex brain activity and cognitive variability
4)Synchronization in complex networks
5)Individual vs. collective human dynamics

1) Complex neural networks and structure-function relationship

Cells in the neural systems interact through synapses, forming fairly complex networks across various scales, from local neuronal circuit up to the cortico-cortical networks linked by long-range projections (white matters). Basing on available data, it has been shown that neural networks display the characteristics of many real world networks, such as small-world properties, hubs and modules. We are interested in exploring special organization features in neural networks, their functional implications and the constraints underlying the formation of such network features. Graph-theory, dynamical modeling and combinatory optimization approaches are developed and applied to study how complex networks emerging under the constraints can satisfy the basic requirement for efficient information processing through diverse dynamical activities.

Related publications

G. Zamora-Lopez, C.S. Zhou and J. Kurths, "Exploring brain function from anatomical connectivity". Frontiers in Neuroscience 5, 83 (2011) (Invited Review).

G. Zamora-Lopez, C.S. Zhou, and J. Kurths, "Cortical hubs form a module for multisensory integration on top of the hierarchy of cortical networks" , Frontiers in Neuroinformatics, 4, article 1 (2010).

G. Zamora-Lopez, C.S. Zhou, and J. Kurths, "Graph Analysis of Cortical Networks Reveals Complex Anatomical Communication Substrate" , Chaos 19, 015117 (2009).

C.S. Zhou, L. Zemanova, G. Zamora, C.C. Hilgetag and J. Kurths, "Hierarchical organization unveiled by functional connectivity in complex brain networks", Phys. Rev. Lett. 97, 238103 (2006).

L. Zemanova, C.S. Zhou and J. Kurths, "Structural and functional clusters of complex brain networks", Physica D 224, 202 (2006).

2) Self-organized activity and information processing in complex neural networks

Cerebral cortical brain networks possess a number of prominent features of structure and dynamics. Firstly, they are structured as hierarchical modular networks, from large-scale regions of the brain, via cortical areas and area sub-compartments organized as structural and functional maps, to cortical columns, and finally circuits made up of individual neurons. A balance of excitation and inhibition also features local recurrent neural networks. Second, the networks display self-organized sustained activity, which is persistent in the absence of external stimuli. At systems level, such activities are characterized by complex rhythmical oscillations over a broadband background, while at the cellular level or mesoscales, neuronal discharges display avalanches, indicating that cortical networks are at the self-organized critical states. We are interested in understanding how such highly fluctuating activities are organized in biologically realistic complex neural network models and how they are employed in neural information processing and learning. As the first step, we have shown that hierarchical modular network organization has important impact on self-organized critical dynamics. Our research will be focusing on the impact of such fluctuating spatial-temporal patterns on the timing of neuronal firing, and on the structure-dynamics co-evolution due to neural plasticity, different from information processing using attractor dynamics in connectionist's artificial neural network models.

Related publications

S.J. Wang and C.S. Zhou, "Hierarchical modular structure enhances the robustness of self-organized criticality in neural networks" , New J. Phys. 14, 023005 (2012).

S. Wang, C.C. Hilgetag and C.S. Zhou, "Sustained activity in hierarchical modular neural networks: self-organized criticality and oscillations", Frontiers in Computational Neuroscience, 5, 30 (2011).

3) Complex brain activity and cognitive variability

The brain displays complex, spontaneous ongoing background activity and generates stimulus-induced responses, which are likely to interact nontrivially with each other, since neural network in the brain is a system of interacting nonlinear elements by biophysical and physiological nature. Largely, complex brain activity is analyzed with two groups of methods in order to search for correlates to brain functions. Classical cognitive theory assumes that these two activities are independent of each other and regards the background activity as noise which is eliminated by averaging over many trials of electroencephalographic (EEG) records to obtain the event-related potential (ERP) for a given stimulus condition. Alternative hypotheses assume that the oscillation components, such as alpha and gamma waves, are correlated with cognitive functions; time-frequency and phase are analyzed to search for changes in spectra and phase coherence during cognitive processing. These two branches of approaches and methods pay attention to different aspects of complex brain activity, but both explore only part of the rich information. An evident limitation of ERPs is that they cannot address strong cognitive variability across trials and individual subjects.

In close collaboration with cognitive neuroscientist Prof. Werner Sommer from Berlin Humboldt University, we are interested in analyzing the interaction between ERP and ongoing brain activity, since it is crucial for understanding how the ongoing brain activity impacts on cognitive processing. We take the response variability in cognitive experiments as the window for studying this important problem. There is a long-lasting problem in cognitive neuroscience that cognitive sub-processes, such as stimulus perception, decision-making and motor execution, have strong variability in latency and the conventional averaging ERP method will mix the components associated to the cognitive sub-processes. Recently, we have developed a new method called Residual Iteration Decomposition (RIDE) which can decompose single trial brain activity into several components associated to sub-processes and identify their latencies respectively. This method will have great many applications in cognitive experiments.

Our next steps are to study the nonlinear interaction between ERP and ongoing activity by analyzing the dependence of component latencies on amplitude, phase and synchronization of ongoing activity. This will allow us to obtain much more information from the complex brain activity and its relationship with the functional performance.

We will use modeling to obtain understanding of the mechanism underlying the response variability, which can help us develop new methods to better understand the experimental data.

Related publications

G. Ouyang, G. Hermann, C.S. Zhou and W. Sommer, "Residue Iteration Decomposition (RIDE): a new Method to Separate ERP Components on the Basis of Latency Variability in Single Trials" , Psychophysiology, 48, 1631-1647 (2011).

4) Synchronization in complex networks

Oscillation and synchronization are relevant to many physical, biological and social systems, especially the information processing in neural systems. Previous works in the literature mainly consider complete synchronization of whole networks. Our current interest is in studying more complex partial synchronization states that allow both information segregation and integration, and applying such concepts in understanding the structure-function relationship in neural systems.

Related publications

M. Zhao, C.S. Zhou, J.H Lu and C.H. Lai, "Competition between intracommunity and intercommunity synchronization and relevance in brain cortical networks", Phys. Rev. E, 84, 016109 (2011).

M. Zhao, C.S. Zhou, Y.H. Chen, B. Hu, and B. Wang, "Complexity versus modularity and heterogeneity in oscillatory networks: Combining segregation and integration in neural systems", Physical Review E, 82, 046225 (2010).

T. Zhou, M. Zhao and C.S. Zhou, "Synchronization in effective networks", New J. Phys., 12, 043030 (2010).

J. Zhang, C.S. Zhou, X.K. Xu, and M. Small, "Mapping from structure to dynamics: A unified view of dynamical processes on networks", Phys. Rev. E. 82, 026116 (2010).

C.S. Zhou and J. Kurths, "Dynamical weights and enhanced synchronization in adaptive complex networks", Phys. Rev. Lett. 96, 164102 (2006).

C.S. Zhou, A.E. Motter and J. Kurths, "Universality in the synchronization of weighted random networks", Phys. Rev. Lett. 96, 034101 (2006).

A.E. Motter, C.S. Zhou and J. Kurths, "Network synchronization, diffusion, and the paradox of heterogeneity", Phys. Rev. E 71, 016116 (2005).

5) Individual vs. collective human dynamics

Interacting human activities underlie the patterns of many social, technological, and economic phenomena. Individual humans participate in various activities every day in an apparently random manner. Recent evidence from various deliberate human activity patterns, such as e-mail and letter communications and Web surfing, has shown that human activities are non-Poissonian, with bursts of frequent actions separated by long periods of inactivity, leading to power-law heavy tails in the distributions of inter-event time. We are interested in understanding the impact of interaction between humans on the relationship between individual and collective human dynamics by analyzing and modeling empirical human activity data.

Related publications

Y. Wu, C.S. Zhou, J. Xiao, J. Kurths and H.J. Schellnhuber, "Evidence for a bimodal distribution in human communication", Proc Natl Acad Sci USA, 107, 18803 (2010).

Y. Wu, C.S. Zhou, M.Y. Chen and J. Kurths, "Human comment dynamics in on-line social systems", Physica A, 398, 5832 (2010).