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16th APCA International Conference on Automatic Control and Soft Computing, CONTROLO 2024

作者： Schlarb, Markus Department of Mathematics Julius-Maximilians-Universität Würzburg Würzburg Germany Center for Signal Analysis of Complex Systems Ansbach University of Applied Sciences Ansbach Germany

ISBN: (纸本)9783031817236

The manifold of essential matrices is equipped with a one-parameter family of (pseudo-)Riemannian metrics. For the whole family, explicit formulas for geodesics are derived. Moreover, specific curves, so-called quasi-geodesics, are studied and a closed form expression for a quasi-geodesic connecting two given essential matrices is obtained. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： (pseudo-)Riemannian metrics computer vision essential matrix geodesics quasi-geodesics

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Validating a Chaos Based PRBG Under Different Chaotic Maps

Validating a Chaos Based PRBG Under Different Chaotic Maps

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2024 Panhellenic Conference on Electronics and Telecommunications, PACET 2024

作者： Moysis, Lazaros Lawnik, Marcin Volos, Christos Baptista, Murilo S. Fragulis, George F. Goudos, Sotirios K. University of Western Macedonia Department of Electrical and Computer Engineering Kozani Greece Aristotle University of Thessaloniki Laboratory of Nonlinear Systems - Circuits and Complexity Physics Department Thessaloniki Greece University of Western Macedonia Department of Mechanical Engineering Kozani Greece Silesian University of Technology Faculty of Applied Mathematics Department of Mathematics Applications and Methods for Artificial Intelligence Gliwice44-100 Poland Supa University of Aberdeen Institute for Complex Systems and Mathematical Biology Department of Physics AberdeenAB24 3UX United Kingdom Aristotle University of Thessaloniki ELEDIA@AUTH Physics Department Thessaloniki Greece

ISBN: (纸本)9798350318845

Chaos-based random bit generators are abundantly used in chaos-based encryption and security applications, as a fast, deterministic source of randomness, to perform actions like permutation and substitution. The chaotic map used as a source of randomness though may heavily affect the bit generator's statistical randomness, key space, and speed. Thus, any given bit generator may not be equally efficient for all the chaotic maps used as a seed. Motivated by this, the present work considers a bit generator that utilizes a common modulo-based hashing technique, and studies its performance under a plethora of different chaotic maps. For each map, the generator is evaluated with respect to randomness, key space, and operations per bit ratio. This analysis can serve as a guideline for random bit generator usage in future chaos-based encryption designs. © 2024 IEEE.

关键词： Cryptography

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Partial Stabilization of Nonlinear systems along a Given Trajectory

Partial Stabilization of Nonlinear Systems along a Given Tra...

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European Control Conference (ECC)

作者： Victoria Grushkovska Iryna Vasylieva Alexander Zuyev Department of Mathematics University of Klagenfurt Klagenfurt Austria National Academy of Sciences of Ukraine Institute of Applied Mathematics & Mechanics Sloviansk Ukraine Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany

ISBN: (数字)9783907144107

ISBN: (纸本)9798331540920

In this paper, the problem of partial stabilization of nonlinear systems along a given trajectory is considered. This problem is treated within the framework of stability of a family of sets. Sufficient conditions for the asymptotic stability of a one-parameter family of sets, using time-varying feedback control with trigonometric functions, are derived. The obtained results are applied to a model mechanical system.

关键词： Asymptotic stability Sufficient conditions Europe Control systems Stability analysis Trajectory Feedback control

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Higher-order interactions induce stepwise explosive phase transitions

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Physical Review E 2025年第2期111卷 024303-024303页

作者： Xueqi Li Palash Kumar Pal Youming Lei Dibakar Ghosh Michael Small School of Mathematics and Statistics Northwestern Polytechnical University Xi'an 710072 China Physics and Applied Mathematics Unit Indian Statistical Institute 203B. T. Road Kolkata 700108 India Ministry of Industry and Information Technology Key Laboratory of Dynamics and Control of Complex Systems Northwestern Polytechnical University Xi'an 710072 China Complex Systems Group Department of Mathematics and Statistics The University of Western Australia Crawley WA 6009 Australia Mineral Resources CSIRO Kensington WA 6151 Australia

In recent studies, it has been established that higher-order interactions in coupled oscillators can induce a process from continuous to explosive phase transition. In this study, we identify a phase transition, termed the stepwise explosive phase transition, characterized by the emergence of multiple critical phase plateaus in a globally frequency-weighted coupled pendulum model. This transition bridges the continuous and explosive phase transitions, arising from a delicate balance between attractive higher-order interactions and repulsive pairwise interactions. Specifically, the stepwise explosive phase transition occurs when the higher-order coupling is moderate, neither large nor small, while the pairwise interactions remain repulsive. Our analysis shows that stronger attractive higher-order interactions necessitate weaker repulsive pairwise interactions, leading to partial frequency locking among oscillators and triggering the stepwise transition. We construct an analytical framework using self-consistent equations to provide an approximation of the steady-state behavior. This study uncovers an alternative pathway to the desynchronization, and it provides additional insights into the phase transitions in coupled dynamical networks.

关键词： Pendulums

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Adaptive-triggered H∞ sliding-mode optimal control for nonlinear input-limited systems

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Communications in Nonlinear Science and Numerical Simulation 2025年 149卷

作者： Zhang, Hongxu Wang, Honggui Department of Applied Mathematics Harbin University of Science and Technology Harbin150080 China Heilongjiang Provincial Key Laboratory of Optimization Control and Intelligent Analysis for Complex Systems Harbin University of Science and Technology Harbin150080 China

This paper concentrates on the H∞ sliding mode optimal control (SMOC) problem for nonlinear systems with mismatched interference and constrained input. Firstly, an adaptive-triggered strategy for the discontinuous control part is employed, which can suppress input interference and the separated matched disturbances. Also, the system trajectories are guaranteed to converge to the sliding manifold. Moreover, the adaptive-triggered strategy is optimized into self-triggered strategy with the aim to avoid the real-time measurement of triggered conditions, and the minimum time interval is obtained to prevent Zeno phenomenon. Subsequently, the optimal H∞ control problem of sliding motion turns into a two-person ZS game issue. To derive the solutions of event-trigger HJI equation, an adaptive dynamic programming (ADP) algorithm with critic-only structure is implemented to obtain the optimal control online. Furthermore, by utilizing the Lyapunov technique, the uniformly ultimately bounded (UUB) conditions about system state and the weight estimation error are obtained. At last, simulation outcomes are analyzed to validate the effectiveness of the control strategy. © 2025 Elsevier B.V.

关键词： Sliding mode control

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Strategies for protecting of multilayer networks from group and system-wide targeted attacks

arXiv

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arXiv 2022年

作者： Polishchuk, Olexandr Laboratory of Modeling and Optimization of Complex Systems Pidstryhach Institute for Applied Problems of Mechanics and Mathematics National Academy of Sciences of Ukraine Lviv Ukraine

On the basis of structural model of intersystem interactions, the main local and global structural characteristics of nodes of the multilayer network (MLN) are determined. The notions of weighted and binary aggregate-networks of MLN are introduced and integral indicators of the importance of nodes of the multilayer network are determined. The effectiveness of application of aggregate-networks for solving a number of practically important problems of the theory of complex networks is shown. To determine the most important components of intersystem interactions structure, the concepts of p-core of multilayer network and kag-core of its weighted aggregate-network are introduced. The effective scenarios of successive and simultaneous group attacks on the structure of multilayer network systems have been built based on the use of these cores. Indicators of the importance of separate layers of MLN are introduced and approaches to building scenarios of successive and simultaneous system-wide attacks on the structure of intersystem interactions are formulated. © 2022, CC BY.

关键词： complex networks

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About group and system-wide lesions of complex network systems and intersystem interactions

arXiv

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arXiv 2022年

The main types of negative internal and external influences on complex network systems (NS) and intersystem interactions in monoflow partially overlapped multilayer network systems (MLNS) are analyzed. Among such influences, targeted attacks on real complex systems and their non-targeted damages of various nature are primarily singled out. On the basis of structural and flow models of NS and MLNS, sequential and simultaneous local, group and system-wide damages to the structure and operation process of complex network systems and intersystem interactions are considered. The existing structural and functional scenarios of consecutive attacks on the most important components of the system and the need to neutralize the sources of such attacks as one of the means of system protection are analyzed. The peculiarities of application of such scenarios for the protection of NS and MLNS from system-wide non-target lesions are considered. Approaches to evaluation and overcoming the consequences of negative impacts on the structure and operation process of complex network systems and intersystem interactions are proposed. © 2022, CC BY.

关键词： complex networks

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Quantum entanglement in the multicritical disordered Ising model

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Physical Review B 2024年第21期109卷 214202-214202页

作者： István A. Kovács Department of Physics and Astronomy Northwestern University Evanston 60208 IL United States Northwestern Institute on Complex Systems Northwestern University Evanston 60208 IL United States Department of Engineering Sciences and Applied Mathematics Northwestern University Evanston 60208 IL United States

Quantum entanglement at critical points is often marked by universal characteristics. Here, the entanglement entropy is calculated at the quantum multicritical point of the random transverse-field Ising model (RTIM). We use an efficient implementation of the strong disorder renormalization group method in two and three dimensions for two types of disorder. For cubic subsystems we find a universal logarithmic corner contribution to the area law bln(ℓ) that is independent of the form of disorder. Our results agree qualitatively with those at the quantum critical points of the RTIM, but with new b prefactors due to having both geometric and quantum fluctuations at play. By studying the vicinity of the multicritical point, we demonstrate that the corner contribution serves as an “entanglement susceptibility,” a useful tool to locate the phase transition and to measure the correlation length critical exponents.

关键词： Critical phenomena Quantum entanglement Quantum information theory Quantum phase transitions Coarse graining Finite-size scaling Ising model Numerical Renormalization Group Renormalization group Scaling methods

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THE WEIGHTED AND SHIFTED SEVEN-STEP BDF METHOD FOR PARABOLIC EQUATIONS

arXiv

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arXiv 2024年

作者： Akrivis, Georgios Chen, Minghua Yu, Fan Department of Computer Science and Engineering University of Ioannina Ioannina451 10 Greece Institute of Applied and Computational Mathematics FORTH Heraklion Crete700 13 Greece School of Mathematics and Statistics Gansu Key Laboratory of Applied Mathematics and Complex Systems Lanzhou University Lanzhou730000 China

Stability of the BDF methods of order up to five for parabolic equations can be established by the energy technique via Nevanlinna–Odeh multipliers. The nonexistence of Nevanlinna–Odeh multipliers makes the six-step BDF method special;however, the energy technique was recently extended by the authors in [Akrivis et al., SIAM J. Numer. Anal. 59 (2021) 2449–2472] and covers all six stable BDF methods. The seven-step BDF method is unstable for parabolic equations, since it is not even zero-stable. In this work, we construct and analyze a stable linear combination of two non zero-stable schemes, the seven-step BDF method and its shifted counterpart, referred to as WSBDF7 method. The stability regions of the WSBDFq, q 6 7, with a weight ϑ > 1, increase as ϑ increases, are larger than the stability regions of the classical BDFq, corresponding to ϑ = 1. We determine novel and suitable multipliers for the WSBDF7 method and establish stability for parabolic equations by the energy technique. The proposed approach is applicable for mean curvature flow, gradient flows, fractional equations and nonlinear equations. Copyright © 2024, The Authors. All rights reserved.

关键词： Nonlinear equations

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Construction of Piecewise Chaotic Maps With Tunable Statistical Mean 12

Construction of Piecewise Chaotic Maps With Tunable Statisti...

引用

12th International Conference on Modern Circuits and systems Technologies, MOCAST 2023

作者： Moysis, Lazaros Lawnik, Marcin Baptista, Murilo S. Goudos, Sotirios Volos, Christos Aristotle University of Thessaloniki Laboratory of Nonlinear Systems - Circuits & Complexity Physics Department Thessaloniki Greece University of Western Macedonia Department of Mechanical Engineering Kozani Greece Silesian University of Technology Faculty of Applied Mathematics Department of Mathematics Applications and Methods for Artifiial Intelligence Gliwice44-100 Poland University of Aberdeen Institute for Complex Systems and Mathematical Biology SUPA AberdeenAB24 3UX United Kingdom Aristotle University of Thessaloniki Physics Department Thessaloniki54124 Greece

ISBN: (纸本)9798350321074

In numerous chaos based applications, it is often important to use chaotic maps that showcase desirable statistical characteristics, that can improve the performance of the designed architecture. Yet, it is hard to design maps that can achieve the desired statistical properties. Motivated by this, this work considers a family of piecewise chaotic maps, and studies how tuning their parameters can affect the mean value of the generated chaotic trajectories. Such a family of maps can be highly practical in future chaos based applications. © 2023 IEEE.

关键词： Cryptography

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