Matching Items (4)
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- All Subjects: nonlinear dynamics
- Creators: Lai, Ying-Cheng
Description
This dissertation treats a number of related problems in control and data analysis of complex networks.
First, in existing linear controllability frameworks, the ability to steer a network from any initiate state toward any desired state is measured by the minimum number of driver nodes. However, the associated optimal control energy can become unbearably large, preventing actual control from being realized. Here I develop a physical controllability framework and propose strategies to turn physically uncontrollable networks into physically controllable ones. I also discover that although full control can be guaranteed by the prevailing structural controllability theory, it is necessary to balance the number of driver nodes and control energy to achieve actual control, and my work provides a framework to address this issue.
Second, in spite of recent progresses in linear controllability, controlling nonlinear dynamical networks remains an outstanding problem. Here I develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability. The control objective is to apply parameter perturbation to drive the system from one attractor to another. I introduce the concept of attractor network and formulate a quantifiable framework: a network is more controllable if the attractor network is more strongly connected. I test the control framework using examples from various models and demonstrate the beneficial role of noise in facilitating control.
Third, I analyze large data sets from a diverse online social networking (OSN) systems and find that the growth dynamics of meme popularity exhibit characteristically different behaviors: linear, “S”-shape and exponential growths. Inspired by cell population growth model in microbial ecology, I construct a base growth model for meme popularity in OSNs. Then I incorporate human interest dynamics into the base model and propose a hybrid model which contains a small number of free parameters. The model successfully predicts the various distinct meme growth dynamics.
At last, I propose a nonlinear dynamics model to characterize the controlling of WNT signaling pathway in the differentiation of neural progenitor cells. The model is able to predict experiment results and shed light on the understanding of WNT regulation mechanisms.
First, in existing linear controllability frameworks, the ability to steer a network from any initiate state toward any desired state is measured by the minimum number of driver nodes. However, the associated optimal control energy can become unbearably large, preventing actual control from being realized. Here I develop a physical controllability framework and propose strategies to turn physically uncontrollable networks into physically controllable ones. I also discover that although full control can be guaranteed by the prevailing structural controllability theory, it is necessary to balance the number of driver nodes and control energy to achieve actual control, and my work provides a framework to address this issue.
Second, in spite of recent progresses in linear controllability, controlling nonlinear dynamical networks remains an outstanding problem. Here I develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability. The control objective is to apply parameter perturbation to drive the system from one attractor to another. I introduce the concept of attractor network and formulate a quantifiable framework: a network is more controllable if the attractor network is more strongly connected. I test the control framework using examples from various models and demonstrate the beneficial role of noise in facilitating control.
Third, I analyze large data sets from a diverse online social networking (OSN) systems and find that the growth dynamics of meme popularity exhibit characteristically different behaviors: linear, “S”-shape and exponential growths. Inspired by cell population growth model in microbial ecology, I construct a base growth model for meme popularity in OSNs. Then I incorporate human interest dynamics into the base model and propose a hybrid model which contains a small number of free parameters. The model successfully predicts the various distinct meme growth dynamics.
At last, I propose a nonlinear dynamics model to characterize the controlling of WNT signaling pathway in the differentiation of neural progenitor cells. The model is able to predict experiment results and shed light on the understanding of WNT regulation mechanisms.
ContributorsWang, Lezhi (Author) / Lai, Ying-Cheng (Thesis advisor) / Wang, Xiao (Thesis advisor) / Papandreoou-Suppappola, Antonia (Committee member) / Brafman, David (Committee member) / Arizona State University (Publisher)
Created2017
Description
Conductance fluctuations associated with quantum transport through quantumdot systems are currently understood to depend on the nature of the corresponding classical dynamics, i.e., integrable or chaotic. There are a couple of interesting phenomena about conductance fluctuation and quantum tunneling related to geometrical shapes of graphene systems. Firstly, in graphene quantum-dot systems, when a magnetic field is present, as the Fermi energy or the magnetic flux is varied, both regular oscillations and random fluctuations in the conductance can occur, with alternating transitions between the two. Secondly, a scheme based on geometrical rotation of rectangular devices to effectively modulate the conductance fluctuations is presented. Thirdly, when graphene is placed on a substrate of heavy metal, Rashba spin-orbit interaction of substantial strength can occur. In an open system such as a quantum dot, the interaction can induce spin polarization. Finally, a problem using graphene systems with electron-electron interactions described by the Hubbard Hamiltonian in the setting of resonant tunneling is investigated.
Another interesting problem in quantum transport is the effect of disorder or random impurities since it is inevitable in real experiments. At first, for a twodimensional Dirac ring, as the disorder density is systematically increased, the persistent current decreases slowly initially and then plateaus at a finite nonzero value, indicating remarkable robustness of the persistent currents, which cannot be discovered in normal metal and semiconductor rings. In addition, in a Floquet system with a ribbon structure, the conductance can be remarkably enhanced by onsite disorder.
Recent years have witnessed significant interest in nanoscale physical systems, such as semiconductor supperlattices and optomechanical systems, which can exhibit distinct collective dynamical behaviors. Firstly, a system of two optically coupled optomechanical cavities is considered and the phenomenon of synchronization transition associated with quantum entanglement transition is discovered. Another useful issue is nonlinear dynamics in semiconductor superlattices caused by its key potential application lies in generating radiation sources, amplifiers and detectors in the spectral range of terahertz. In such a system, transition to multistability, i.e., the emergence of multistability with chaos as a system parameter passes through a critical point, is found and argued to be abrupt.
Another interesting problem in quantum transport is the effect of disorder or random impurities since it is inevitable in real experiments. At first, for a twodimensional Dirac ring, as the disorder density is systematically increased, the persistent current decreases slowly initially and then plateaus at a finite nonzero value, indicating remarkable robustness of the persistent currents, which cannot be discovered in normal metal and semiconductor rings. In addition, in a Floquet system with a ribbon structure, the conductance can be remarkably enhanced by onsite disorder.
Recent years have witnessed significant interest in nanoscale physical systems, such as semiconductor supperlattices and optomechanical systems, which can exhibit distinct collective dynamical behaviors. Firstly, a system of two optically coupled optomechanical cavities is considered and the phenomenon of synchronization transition associated with quantum entanglement transition is discovered. Another useful issue is nonlinear dynamics in semiconductor superlattices caused by its key potential application lies in generating radiation sources, amplifiers and detectors in the spectral range of terahertz. In such a system, transition to multistability, i.e., the emergence of multistability with chaos as a system parameter passes through a critical point, is found and argued to be abrupt.
ContributorsYing, Lei (Author) / Lai, Ying-Cheng (Thesis advisor) / Vasileska, Dragica (Committee member) / Chen, Tingyong (Committee member) / Yao, Yu (Committee member) / Arizona State University (Publisher)
Created2016
Description
Predicting nonlinear dynamical systems has been a long-standing challenge in science. This field is currently witnessing a revolution with the advent of machine learning methods. Concurrently, the analysis of dynamics in various nonlinear complex systems continues to be crucial. Guided by these directions, I conduct the following studies. Predicting critical transitions and transient states in nonlinear dynamics is a complex problem. I developed a solution called parameter-aware reservoir computing, which uses machine learning to track how system dynamics change with a driving parameter. I show that the transition point can be accurately predicted while trained in a sustained functioning regime before the transition. Notably, it can also predict if the system will enter a transient state, the distribution of transient lifetimes, and their average before a final collapse, which are crucial for management. I introduce a machine-learning-based digital twin for monitoring and predicting the evolution of externally driven nonlinear dynamical systems, where reservoir computing is exploited. Extensive tests on various models, encompassing optics, ecology, and climate, verify the approach’s effectiveness. The digital twins can extrapolate unknown system dynamics, continually forecast and monitor under non-stationary external driving, infer hidden variables, adapt to different driving waveforms, and extrapolate bifurcation behaviors across varying system sizes. Integrating engineered gene circuits into host cells poses a significant challenge in synthetic biology due to circuit-host interactions, such as growth feedback. I conducted systematic studies on hundreds of circuit structures exhibiting various functionalities, and identified a comprehensive categorization of growth-induced failures. I discerned three dynamical mechanisms behind these circuit failures. Moreover, my comprehensive computations reveal a scaling law between the circuit robustness and the intensity of growth feedback. A class of circuits with optimal robustness is also identified. Chimera states, a phenomenon of symmetry-breaking in oscillator networks, traditionally have transient lifetimes that grow exponentially with system size. However, my research on high-dimensional oscillators leads to the discovery of ’short-lived’ chimera states. Their lifetime increases logarithmically with system size and decreases logarithmically with random perturbations, indicating a unique fragility. To understand these states, I use a transverse stability analysis supported by simulations.
ContributorsKong, Lingwei (Author) / Lai, Ying-Cheng (Thesis advisor) / Tian, Xiaojun (Committee member) / Papandreou-Suppappola, Antonia (Committee member) / Alkhateeb, Ahmed (Committee member) / Arizona State University (Publisher)
Created2023
Description
Complex dynamical systems are the kind of systems with many interacting components that usually have nonlinear dynamics. Those systems exist in a wide range of disciplines, such as physical, biological, and social fields. Those systems, due to a large amount of interacting components, tend to possess very high dimensionality. Additionally, due to the intrinsic nonlinear dynamics, they have tremendous rich system behavior, such as bifurcation, synchronization, chaos, solitons. To develop methods to predict and control those systems has always been a challenge and an active research area.
My research mainly concentrates on predicting and controlling tipping points (saddle-node bifurcation) in complex ecological systems, comparing linear and nonlinear control methods in complex dynamical systems. Moreover, I use advanced artificial neural networks to predict chaotic spatiotemporal dynamical systems. Complex networked systems can exhibit a tipping point (a “point of no return”) at which a total collapse occurs. Using complex mutualistic networks in ecology as a prototype class of systems, I carry out a dimension reduction process to arrive at an effective two-dimensional (2D) system with the two dynamical variables corresponding to the average pollinator and plant abundances, respectively. I demonstrate that, using 59 empirical mutualistic networks extracted from real data, our 2D model can accurately predict the occurrence of a tipping point even in the presence of stochastic disturbances. I also develop an ecologically feasible strategy to manage/control the tipping point by maintaining the abundance of a particular pollinator species at a constant level, which essentially removes the hysteresis associated with tipping points.
Besides, I also find that the nodal importance ranking for nonlinear and linear control exhibits opposite trends: for the former, large degree nodes are more important but for the latter, the importance scale is tilted towards the small-degree nodes, suggesting strongly irrelevance of linear controllability to these systems. Focusing on a class of recurrent neural networks - reservoir computing systems that have recently been exploited for model-free prediction of nonlinear dynamical systems, I uncover a surprising phenomenon: the emergence of an interval in the spectral radius of the neural network in which the prediction error is minimized.
My research mainly concentrates on predicting and controlling tipping points (saddle-node bifurcation) in complex ecological systems, comparing linear and nonlinear control methods in complex dynamical systems. Moreover, I use advanced artificial neural networks to predict chaotic spatiotemporal dynamical systems. Complex networked systems can exhibit a tipping point (a “point of no return”) at which a total collapse occurs. Using complex mutualistic networks in ecology as a prototype class of systems, I carry out a dimension reduction process to arrive at an effective two-dimensional (2D) system with the two dynamical variables corresponding to the average pollinator and plant abundances, respectively. I demonstrate that, using 59 empirical mutualistic networks extracted from real data, our 2D model can accurately predict the occurrence of a tipping point even in the presence of stochastic disturbances. I also develop an ecologically feasible strategy to manage/control the tipping point by maintaining the abundance of a particular pollinator species at a constant level, which essentially removes the hysteresis associated with tipping points.
Besides, I also find that the nodal importance ranking for nonlinear and linear control exhibits opposite trends: for the former, large degree nodes are more important but for the latter, the importance scale is tilted towards the small-degree nodes, suggesting strongly irrelevance of linear controllability to these systems. Focusing on a class of recurrent neural networks - reservoir computing systems that have recently been exploited for model-free prediction of nonlinear dynamical systems, I uncover a surprising phenomenon: the emergence of an interval in the spectral radius of the neural network in which the prediction error is minimized.
ContributorsJiang, Junjie (Author) / Lai, Ying-Cheng (Thesis advisor) / Papandreou-Suppappola, Antonia (Committee member) / Wang, Xiao (Committee member) / Zhang, Yanchao (Committee member) / Arizona State University (Publisher)
Created2020