Minvydas Ragulskis 教授系列研究生学术报告通知
系列报告题目： Nonlinear Dynamical Systems – Problems and Applications
报 告 人： Minvydas Ragulskis教授, 立陶宛考纳斯科技大学
主办单位：江苏省力学学会学术工作委员会、河海大学力学与材料学院
地 点：南京市江宁区佛城西路8号 河海大学 江宁校区
系列报告时间地点安排：
系列研究生学术报告简介：
This series is focused on the theory and applications of nonlinear dynamical systems. The topics range from time series analysis, dynamic visual cryptography, to temporary stabilization of unstable attractors. Each lecture provides an insight into the state of the art in the field, discusses original solutions and applications, and presents open problems for the future research. The lecture series is oriented towards doctoral degree students and researchers working in the diverse field of nonlinear dynamics.
报告人简介:
Minvydas Ragulskis is the professor of Applied Mathematics at Kaunas University of Technology, full professor at the Department of Mathematical Modelling since 2002. Also, he is the member elect, Lithuanian Academy of Sciences, author of 100+ articles in SCIE Journals, member of more than 30 committees of International Conferences, Invited and Keynote speaker at several major International Conferences. Professor Minvydas is a member of Horizon 2020 Expert Panels at European Commission for evaluation of European research proposals, invited reviewer for 30+ International Journals. His research interests including nonlinear dynamics and chaos, mathematical and computational analysis of nonlinear systems.
Minvydas Ragulskis 教授系列研究生学术报告摘要
报告题目一： Time series analysis – attractor embedding and evolutionary prediction.
时 间： 2016年6月14日（周二）下午15:00-17:00
地 点： 乐学楼832
报告一摘要：
Time series forecasting, especially long-term prediction, is a challenge in many fields of science and engineering. Many techniques exist for time series forecasting. This lecture presents latest results in this demanding and very competitive research direction. Two different time series forecasting approaches are presented in this lecture – long time series – and short time series predictors. Nonlinear time series analysis techniques are exploited for the construction of long term time series predictors. And a new approach to short term time series prediction is presented as an evolutionary problem of the reconstruction of near-optimal algebraic skeletons. Short time series prediction techniques are also used for time series segmentation and smoothing applications. Computational experiments are used to illustrate the efficiency and effectiveness of the proposed predictors – as well to validate the reconstructed dynamical models of the analyzed time series.
报告题目二： Solitary solutions to nonlinear differential equations – computational framework and applications.
时 间： 2016年6月17日（周五）上午9:50-12:15
地 点： 乐学楼832
报告二摘要：
This lecture presents latest research results in the area of construction of solitary solutions to nonlinear differential equations. Solitary waves (also called solitons) are an important phenomenon in mathematical physics, which are now considered one of the most vibrant areas of research in both experimental and theoretical physics. A criterion determining if an analytic solution to a differential equation can be expressed in a form comprising a finite number of exponential functions is constructed. The employment of this criterion also gives an answer on the structure of the solution.
Such analytical techniques can not only provide information on the existence of solitary solutions to nonlinear evolutionary processes. These techniques enable finding new nonlinear effects in biological processes of competing populations, generalize and classify nonlinear differential equations in respect to solitary waves, determine kink, bright and dark solitons in relativistic astrophysical systems. The applicability of the proposed techniques for deriving necessary and sufficient conditions for the existence of solitary solutions is illustrated by a number of computational experiments from a diverse set of physical, engineering and biological systems.
报告题目三： Self-organizing patterns for digital image hiding and communication applications.
时 间： 2016年6月21日（周二）下午15:00-17:00
地 点： 乐学楼832
报告三摘要：
A secure steganographic communication algorithm based on self-organizing patterns is discussed in this lecture. Self-organizing patterns induced by complex interactions between competing individuals are exploited for hiding and transmitting secret visual information. It is shown that the hiding capacity of the system (the minimum size of the detectable primitives and the minimum distance between two primitives) is sufficient for the effective transmission of digital dichotomous images. Also, it is demonstrated that the proposed communication scheme is resilient to time backwards, plain image attacks and is highly sensitive to perturbations of private and public keys. Communication schemes based on the atrial fibrillation model and competitively coupled maps are also shown to be well applicable for such image hiding and communication algorithms. A number of computational experiments are used to demonstrate the effectiveness of the proposed communication schemes.
报告题目四： Attractors, bifurcations and control problems in models of biological neurons and their networks.
时 间： 2016年6月24日（周五）上午9:50-12:15
地 点： 乐学楼832
报告四摘要：
A network of neurons with dendritic dynamics is analyzed in this lecture. Two stable regimes of the complete network can coexist under continuous weak stimulation: the oscillatory synchronized regime and the quiet regime, where all neurons stop firing completely. It is shown that a single control pulse can calm a single neuron as well as the whole network, and the network stays in the quiet regime as long as the weak stimulation is turned on. It is also demonstrated that the same control technique can be effectively used to calm a random Erdos–Renyi network of dendritic neurons. Moreover, it appears that the random network of dendritic neurons can evolve into the quiet regime without applying any external pulse-based control techniques.
Complex nonlinear dynamics is observed when the dendritic neuron undergoes not only phase dependent continuous weak stimulation, but also when it is driven by an external phase-independent stimulation. In the latter case basin boundaries between the synchronized and the quiet regime become complex and fractal. Control strategies based on isolated pulses are not effective in these circumstances, because it becomes difficult to predict the dynamics of the neuron after the application of the control pulse. A new neuron control method is proposed. A weak phase control strategy is applied until fractal basin boundaries evolve into a deterministic manifold. Consequently, a single control pulse is immediately applied and the neuron evolves into the calm state.
报告题目五： Iterative maps of matrices – problems and applications.
时 间： 2016年6月28日（周二）下午15:00-17:00
地 点： 乐学楼832
报告五摘要：
The concept of discrete iterative maps is extended by replacing the scalar variable by a square matrix of variables. Dynamical properties of such iterative maps are explored in detail when the order of matrices is 2. It is shown that the evolution of the logistic map depends not only on the control parameter but also on the eigenvalues of the matrix of initial conditions. Several computational examples are used to demonstrate the convergence to periodic attractors and the sensitivity of chaotic processes to initials conditions.
The effect of explosive divergence in generalized iterative maps of matrices is defined and described using formal algebraic techniques. It is shown that the effect of explosive divergence can be observed in an iterative map of square matrices of order 2 if and only if the matrix of initial conditions is a nilpotent matrix and the Lyapunov exponent of the corresponding scalar iterative map is greater than zero. Computational experiments with the logistic map and the circle map are used to illustrate the effect of explosive divergence occurring in iterative maps of matrices. One of many applications of the iterative maps of matrices - the encryption of optical images - is discussed in details. Computational experiments are used to illustrate the properties of such mappings and their potential applications.
报告题目六： Dynamic visual cryptography – problems and applications.
时 间： 2016年7月1日（周五）上午9:50-12:15
地 点： 乐学楼832
报告六摘要：
Geometric moiré is a classical in-plane whole field nondestructive optical experimental technique based on analysis of visual patterns produced by superposition of two regular gratings that geometrically interfere. Two goals exist in moiré pattern research. The first is the analysis of moiré patterns. The task is to analyze and characterize the distribution of moiré fringes in a moiré pattern. certain predefined moiré pattern is required. The synthesis process involves production of such two images that the required moiré pattern emerges when those images are superimposed. Moiré synthesis and analysis are tightly linked and understanding one task gives insight into the other.
Image hiding based on optical time-averaging moiré technique is presented in this lecture. It is a novel visual decoding scheme when the secret image is embedded into a moiré grating and can be interpreted by a naked eye only when the image is harmonically oscillated in a predefined direction. Phase matching and initial stochastic phase deflection algorithms are used to encrypt the image. The decoding of the image is completely visual. The secret embedded image appears when the encrypted image is oscillated according to a predefined law of motion. Computational and experimental examples are used to demonstrate the functionality of the method.
Image hiding based on time-averaged fringes produced by non-harmonic oscillations and near-optimal moiré are further discussed. The criterion of the optimality of a moiré grating serves as a fitness function for evolutionary algorithms which are used to identify a near-optimal moiré grating for image hiding applications. Numerical experiments are used to illustrate the functionality of the method.
报告题目七： Dynamic visual cryptography – advanced topics.
时 间： 2016年7月5日（周二）下午15:00-17:00
地 点： 乐学楼832
报告七摘要：
Dynamic visual cryptography scheme based on chaotic oscillations is presented in this lecture. Special computational algorithms are required for hiding the secret image in the cover moiré grating, but the decryption of the secret is completely visual. The secret image is leaked in the form of time-averaged geometric moiré fringes when the cover image is oscillated by a chaotic law. The relationship among the standard deviation of the stochastic time variable, the pitch of the moiré grating and the pixel size ensuring visual decryption of the secret is derived. The parameters of these chaotic oscillations must be carefully preselected before the secret image is leaked from the cover image. Several computational experiments are used to illustrate the functionality and the applicability of the proposed image hiding technique.
An optical experimental technique based on dynamic visual cryptography is proposed for the optical assessment of chaotic oscillations. It is demonstrated that this visual scheme is applicable for the assessment of chaotic oscillations even though time-averaged moiré fringes do not form when the encoded cover image is oscillated by the chaotic law. Image hiding schemes in deformable stochastic moiré gratings are discussed in details. Image communication scheme based on dynamic visual cryptography and computer generated holography is discussed and demonstrated using computational experiments.
报告题目八： H-ranks – theory and applications for control of discrete and continuous nonlinear dynamical systems.
时 间： 2016年7月8日（周五）上午9:50-12:15
地 点： 乐学楼832
报告八摘要：
An alternative technique for clocking the convergence of iterative chaotic maps is presented in this lecture. It is based on the concept of the Hankel rank of a solution of the discrete nonlinear dynamical system. Computation and visualization of pseudo-ranks in the space of system’s parameters and initial conditions provides the insight into the fractal nature of the dynamical attractor and reveals the stable, the unstable manifold and the convergence properties of the system. All these manifolds are produced by a simple and a straightforward computational rule and are intertwined in one figure. On the other hand, the computation of ranks of subsequences of solutions helps to identify and assess the sensitivity of the system to initial conditions and can be used as a simple and effective numerical tool for qualitative investigation of discrete iterative maps.
An algebraic approach based on the rank of a sequence is proposed for the exploration of the onset of chaos in discrete nonlinear dynamical systems. The rank of the partial solution is identified and a special technique based on Hankel matrices is used to decompose the solution into algebraic primitives comprising roots of the modified characteristic equation. The distribution of roots describes the dynamical complexity of a solution and is used to explore properties of the nonlinear system and the onset of chaos.
The concept of the H-rank of a scalar sequence is used for the assessment of transient processes of continuous nonlinear dynamical systems. It is demonstrated that the manifold of non-asymptotic convergence to a stable limit cycle also exists in the stroboscopic representation of the transient data of the periodically driven nonlinear pendulum. A method based on a short external impulse is proposed for the control of transient processes when the transition time to stable limit cycles must be minimized.
报 告 人： Minvydas Ragulskis教授, 立陶宛考纳斯科技大学
主办单位：江苏省力学学会学术工作委员会、河海大学力学与材料学院
地 点：南京市江宁区佛城西路8号 河海大学 江宁校区
系列报告时间地点安排：
| 序号 | 时间 | 地点 | 研究生学术报告题目 |
| 1 | 6月14日（周二） 下午15:00-17:00 |
乐学楼832 | Time series analysis – attractor embedding and evolutionary prediction |
| 2 | 6月17日（周五） 上午9:50-12:15 |
乐学楼832 | Solitary solutions to nonlinear differential equations – computational framework and applications |
| 3 | 6月21日（周二） 下午15:00-17:00 |
乐学楼832 | Self-organizing patterns for digital image hiding and communication applications |
| 4 | 6月24日（周五） 上午9:50-12:15 |
乐学楼832 | Attractors, bifurcations and control problems in models of biological neurons and their networks |
| 5 | 6月28日（周二） 下午15:00-17:00 |
乐学楼832 | Iterative maps of matrices – problems and applications |
| 6 | 7月1日（周五） 上午9:50-12:15 |
乐学楼832 | Dynamic visual cryptography – problems and applications |
| 7 | 7月5日（周二） 下午15:00-17:00 |
乐学楼832 | Dynamic visual cryptography – advanced topics |
| 8 | 7月8日（周五） 上午9:50-12:15 |
乐学楼832 | H-ranks – theory and applications for control of discrete and continuous nonlinear dynamical systems |
系列研究生学术报告简介：
This series is focused on the theory and applications of nonlinear dynamical systems. The topics range from time series analysis, dynamic visual cryptography, to temporary stabilization of unstable attractors. Each lecture provides an insight into the state of the art in the field, discusses original solutions and applications, and presents open problems for the future research. The lecture series is oriented towards doctoral degree students and researchers working in the diverse field of nonlinear dynamics.
报告人简介:
Minvydas Ragulskis is the professor of Applied Mathematics at Kaunas University of Technology, full professor at the Department of Mathematical Modelling since 2002. Also, he is the member elect, Lithuanian Academy of Sciences, author of 100+ articles in SCIE Journals, member of more than 30 committees of International Conferences, Invited and Keynote speaker at several major International Conferences. Professor Minvydas is a member of Horizon 2020 Expert Panels at European Commission for evaluation of European research proposals, invited reviewer for 30+ International Journals. His research interests including nonlinear dynamics and chaos, mathematical and computational analysis of nonlinear systems.Minvydas Ragulskis 教授系列研究生学术报告摘要
报告题目一： Time series analysis – attractor embedding and evolutionary prediction.
时 间： 2016年6月14日（周二）下午15:00-17:00
地 点： 乐学楼832
报告一摘要：
Time series forecasting, especially long-term prediction, is a challenge in many fields of science and engineering. Many techniques exist for time series forecasting. This lecture presents latest results in this demanding and very competitive research direction. Two different time series forecasting approaches are presented in this lecture – long time series – and short time series predictors. Nonlinear time series analysis techniques are exploited for the construction of long term time series predictors. And a new approach to short term time series prediction is presented as an evolutionary problem of the reconstruction of near-optimal algebraic skeletons. Short time series prediction techniques are also used for time series segmentation and smoothing applications. Computational experiments are used to illustrate the efficiency and effectiveness of the proposed predictors – as well to validate the reconstructed dynamical models of the analyzed time series.
报告题目二： Solitary solutions to nonlinear differential equations – computational framework and applications.
时 间： 2016年6月17日（周五）上午9:50-12:15
地 点： 乐学楼832
报告二摘要：
This lecture presents latest research results in the area of construction of solitary solutions to nonlinear differential equations. Solitary waves (also called solitons) are an important phenomenon in mathematical physics, which are now considered one of the most vibrant areas of research in both experimental and theoretical physics. A criterion determining if an analytic solution to a differential equation can be expressed in a form comprising a finite number of exponential functions is constructed. The employment of this criterion also gives an answer on the structure of the solution.
Such analytical techniques can not only provide information on the existence of solitary solutions to nonlinear evolutionary processes. These techniques enable finding new nonlinear effects in biological processes of competing populations, generalize and classify nonlinear differential equations in respect to solitary waves, determine kink, bright and dark solitons in relativistic astrophysical systems. The applicability of the proposed techniques for deriving necessary and sufficient conditions for the existence of solitary solutions is illustrated by a number of computational experiments from a diverse set of physical, engineering and biological systems.
报告题目三： Self-organizing patterns for digital image hiding and communication applications.
时 间： 2016年6月21日（周二）下午15:00-17:00
地 点： 乐学楼832
报告三摘要：
A secure steganographic communication algorithm based on self-organizing patterns is discussed in this lecture. Self-organizing patterns induced by complex interactions between competing individuals are exploited for hiding and transmitting secret visual information. It is shown that the hiding capacity of the system (the minimum size of the detectable primitives and the minimum distance between two primitives) is sufficient for the effective transmission of digital dichotomous images. Also, it is demonstrated that the proposed communication scheme is resilient to time backwards, plain image attacks and is highly sensitive to perturbations of private and public keys. Communication schemes based on the atrial fibrillation model and competitively coupled maps are also shown to be well applicable for such image hiding and communication algorithms. A number of computational experiments are used to demonstrate the effectiveness of the proposed communication schemes.
报告题目四： Attractors, bifurcations and control problems in models of biological neurons and their networks.
时 间： 2016年6月24日（周五）上午9:50-12:15
地 点： 乐学楼832
报告四摘要：
A network of neurons with dendritic dynamics is analyzed in this lecture. Two stable regimes of the complete network can coexist under continuous weak stimulation: the oscillatory synchronized regime and the quiet regime, where all neurons stop firing completely. It is shown that a single control pulse can calm a single neuron as well as the whole network, and the network stays in the quiet regime as long as the weak stimulation is turned on. It is also demonstrated that the same control technique can be effectively used to calm a random Erdos–Renyi network of dendritic neurons. Moreover, it appears that the random network of dendritic neurons can evolve into the quiet regime without applying any external pulse-based control techniques.
Complex nonlinear dynamics is observed when the dendritic neuron undergoes not only phase dependent continuous weak stimulation, but also when it is driven by an external phase-independent stimulation. In the latter case basin boundaries between the synchronized and the quiet regime become complex and fractal. Control strategies based on isolated pulses are not effective in these circumstances, because it becomes difficult to predict the dynamics of the neuron after the application of the control pulse. A new neuron control method is proposed. A weak phase control strategy is applied until fractal basin boundaries evolve into a deterministic manifold. Consequently, a single control pulse is immediately applied and the neuron evolves into the calm state.
报告题目五： Iterative maps of matrices – problems and applications.
时 间： 2016年6月28日（周二）下午15:00-17:00
地 点： 乐学楼832
报告五摘要：
The concept of discrete iterative maps is extended by replacing the scalar variable by a square matrix of variables. Dynamical properties of such iterative maps are explored in detail when the order of matrices is 2. It is shown that the evolution of the logistic map depends not only on the control parameter but also on the eigenvalues of the matrix of initial conditions. Several computational examples are used to demonstrate the convergence to periodic attractors and the sensitivity of chaotic processes to initials conditions.
The effect of explosive divergence in generalized iterative maps of matrices is defined and described using formal algebraic techniques. It is shown that the effect of explosive divergence can be observed in an iterative map of square matrices of order 2 if and only if the matrix of initial conditions is a nilpotent matrix and the Lyapunov exponent of the corresponding scalar iterative map is greater than zero. Computational experiments with the logistic map and the circle map are used to illustrate the effect of explosive divergence occurring in iterative maps of matrices. One of many applications of the iterative maps of matrices - the encryption of optical images - is discussed in details. Computational experiments are used to illustrate the properties of such mappings and their potential applications.
报告题目六： Dynamic visual cryptography – problems and applications.
时 间： 2016年7月1日（周五）上午9:50-12:15
地 点： 乐学楼832
报告六摘要：
Geometric moiré is a classical in-plane whole field nondestructive optical experimental technique based on analysis of visual patterns produced by superposition of two regular gratings that geometrically interfere. Two goals exist in moiré pattern research. The first is the analysis of moiré patterns. The task is to analyze and characterize the distribution of moiré fringes in a moiré pattern. certain predefined moiré pattern is required. The synthesis process involves production of such two images that the required moiré pattern emerges when those images are superimposed. Moiré synthesis and analysis are tightly linked and understanding one task gives insight into the other.
Image hiding based on optical time-averaging moiré technique is presented in this lecture. It is a novel visual decoding scheme when the secret image is embedded into a moiré grating and can be interpreted by a naked eye only when the image is harmonically oscillated in a predefined direction. Phase matching and initial stochastic phase deflection algorithms are used to encrypt the image. The decoding of the image is completely visual. The secret embedded image appears when the encrypted image is oscillated according to a predefined law of motion. Computational and experimental examples are used to demonstrate the functionality of the method.
Image hiding based on time-averaged fringes produced by non-harmonic oscillations and near-optimal moiré are further discussed. The criterion of the optimality of a moiré grating serves as a fitness function for evolutionary algorithms which are used to identify a near-optimal moiré grating for image hiding applications. Numerical experiments are used to illustrate the functionality of the method.
报告题目七： Dynamic visual cryptography – advanced topics.
时 间： 2016年7月5日（周二）下午15:00-17:00
地 点： 乐学楼832
报告七摘要：
Dynamic visual cryptography scheme based on chaotic oscillations is presented in this lecture. Special computational algorithms are required for hiding the secret image in the cover moiré grating, but the decryption of the secret is completely visual. The secret image is leaked in the form of time-averaged geometric moiré fringes when the cover image is oscillated by a chaotic law. The relationship among the standard deviation of the stochastic time variable, the pitch of the moiré grating and the pixel size ensuring visual decryption of the secret is derived. The parameters of these chaotic oscillations must be carefully preselected before the secret image is leaked from the cover image. Several computational experiments are used to illustrate the functionality and the applicability of the proposed image hiding technique.
An optical experimental technique based on dynamic visual cryptography is proposed for the optical assessment of chaotic oscillations. It is demonstrated that this visual scheme is applicable for the assessment of chaotic oscillations even though time-averaged moiré fringes do not form when the encoded cover image is oscillated by the chaotic law. Image hiding schemes in deformable stochastic moiré gratings are discussed in details. Image communication scheme based on dynamic visual cryptography and computer generated holography is discussed and demonstrated using computational experiments.
报告题目八： H-ranks – theory and applications for control of discrete and continuous nonlinear dynamical systems.
时 间： 2016年7月8日（周五）上午9:50-12:15
地 点： 乐学楼832
报告八摘要：
An alternative technique for clocking the convergence of iterative chaotic maps is presented in this lecture. It is based on the concept of the Hankel rank of a solution of the discrete nonlinear dynamical system. Computation and visualization of pseudo-ranks in the space of system’s parameters and initial conditions provides the insight into the fractal nature of the dynamical attractor and reveals the stable, the unstable manifold and the convergence properties of the system. All these manifolds are produced by a simple and a straightforward computational rule and are intertwined in one figure. On the other hand, the computation of ranks of subsequences of solutions helps to identify and assess the sensitivity of the system to initial conditions and can be used as a simple and effective numerical tool for qualitative investigation of discrete iterative maps.
An algebraic approach based on the rank of a sequence is proposed for the exploration of the onset of chaos in discrete nonlinear dynamical systems. The rank of the partial solution is identified and a special technique based on Hankel matrices is used to decompose the solution into algebraic primitives comprising roots of the modified characteristic equation. The distribution of roots describes the dynamical complexity of a solution and is used to explore properties of the nonlinear system and the onset of chaos.
The concept of the H-rank of a scalar sequence is used for the assessment of transient processes of continuous nonlinear dynamical systems. It is demonstrated that the manifold of non-asymptotic convergence to a stable limit cycle also exists in the stroboscopic representation of the transient data of the periodically driven nonlinear pendulum. A method based on a short external impulse is proposed for the control of transient processes when the transition time to stable limit cycles must be minimized.
(作者：邬萱 )