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arXiv 2025年

作者： Wagemakers, Alexandre Periwal, Vipul Nonlinear Dynamics Chaos and Complex Systems Group Departamento de Biolog"’ia y Geolog"’ia F"’isica aplicada y Qu"’imica inorg"’anica Universidad Rey Juan Carlos Tulip"’an M"’ostoles Madrid28933 Spain Laboratory of Biological Modeling National Institute of Diabetes and Digestive and Kidney Diseases National Institutes of Health BethesdaMD20892 United States

We explore a family of numerical methods, based on the Steffensen divided difference iterative algorithm, that do not evaluate the derivative of the objective functions. The family of methods achieves second-order convergence with two function evaluations per iteration with marginal additional computational cost. An important side benefit of the method is the improvement in stability for different initial conditions compared to the vanilla Steffensen method. We present numerical results for scalar functions, fields, and scalar fields. This family of methods outperforms the Steffensen method with respect to standard quantitative metrics in most cases. © 2025, CC BY.

关键词： Consensus algorithm

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Review of the Study of nonlinear Atmospheric dynamics in China (1999-2002)

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Advances in Atmospheric Sciences 2004年第3期21卷 399-406页

作者：刁一娜封国林刘式达刘式适罗德海黄思训陆维松丑纪范 Department of Atmospheric and Oceanic Sciences Ocean University of China Qingdao 266003 State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid DynamicsInstitute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 State Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics Institute of Atmospheric Physics Chinese Academy of Sciences Beijing 100029 Department of Atmospheric Sciences Peking University Beijing 100871 Department of Atmospheric and Oceanic Sciences Ocean University of China Qingdao 266003 P. L. A. University of Science & Engineering Meteorological Institute Nanjing 211101 Nanjing Institute of Meteorology Nanjing 210044 Beijing Training Center China Meteorological Administration Beijing 100081esearches on nonlinear atmospheric dynamics in China (1999-2002) are briefly surveyed. This review includes the major achievements in the following branches of nonlinear dynamics: nonlinear stability theory nonlinear blocking dynamics 3D spiral structure in the atmosphere traveling wave solution of the nonlinear evolution equation numerical predictability in a chaotic system and global analysis of climate dynamics. Some applications of nonlinear methods such as hierarchy structure of climate and scaling invariance the spatial-temporal series predictive method the nonlinear inverse problem and a new difference scheme with multi-time Ievels are also introduced.

Researches on nonlinear atmospheric dynamics in China (1999-2002) are briefly surveyed. This review includes the major achievements in the following branches of nonlinear dynamics: nonlinear stability theory, nonlinear blocking dynamics, 3D spiral structure in the atmosphere, traveling wave solution of the nonlinear evolution equation, numerical predictability in a chaotic system, and global analysis of climate dynamics. Some applications of nonlinear methods such as hierarchy structure of climate and scaling invariance, the spatial-temporal series predictive method, the nonlinear inverse problem, and a new difference scheme with multi-time Ievels are also introduced.

关键词： nonlinear dynamics stability blocking spiral structure traveling wave global analysis

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Mathematical modeling of nonlinear dynamics of the cardiovascular system under different physiological conditions 5

Mathematical modeling of nonlinear dynamics of the cardiovas...

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5th Scientific School on dynamics of Complex Networks and their Applications, DCNA 2021

作者： Ishbulatov, Yurii M. Karavaev, Anatoly S. Ponomarenko, Vladimir I. Prokhorov, Mikhail D. Kiselev, Anton R. Bezruchko, Boris P. Laboratory of Nonlinear Dynamics Modelling Saratov Branch of the Institute of RadioEngineering and Electronics of Russian Academy of Sciences Department of Innovative Cardiological Information Technology Institute of Cardiological Research Saratov State Medical University Department of Dynamic Modeling and Biomedical Engineering Saratov State University Saratov Russia Laboratory of Nonlinear Dynamics Modelling Saratov Branch of the Institute of RadioEngineering and Electronics of Russian Academy of Sciences Department of Dynamic Modeling and Biomedical Engineering Saratov State University Saratov Russia Laboratory of Nonlinear Dynamics Modeling Saratov Branch of the Institute of Radio Engineering and Electronics of Russian Academy of Sciences Saratov Russia Department of Innovative Cardiological Information Technology Institute of Cardiological Research Saratov State Medical University Department of Dynamic Modeling and Biomedical Engineering Saratov State University Saratov Russia

ISBN: (纸本)9781665442824

nonlinear dynamics of the cardiovascular system under various physiological conditions is still largely not understood, especially the coupling between the elements of autonomic control and respiration. Under normal, healthy conditions the loops of the autonomic control of the heart rate exhibit intervals of coupled and uncoupled behavior, and during the tests with linearly increasing frequency of respiration, we observed coupling between the respiratory signal and the low-frequency rhythms in the RR-intervals signal associated with the autonomic control of the heart rate. Some researchers theorize that the perceived coupling is due to the presence of the same driving rhythm, which originates from the brain or respiratory system, respectively. Other theory suggest that the observed coupling is based on the phase synchronization between the loops of autonomic control. We applied mathematical modeling to investigate this problem, qualitative and quantitative agreement of the model with the experimental data, suggest that the cardiovascular and cardiorespiratory coupling is based on phase synchronization. © 2021 IEEE

关键词： dynamics

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On finite-time stability of some COVID-19 models using fractional discrete calculus

Computer Methods and Programs in Biomedicine Update

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Computer Methods and Programs in Biomedicine Update 2025年 7卷

作者： Momani, Shaher Batiha, Iqbal M. Bendib, Issam Al-Nana, Abeer Ouannas, Adel Dalah, Mohamed Department of Mathematics Faculty of Science The University of Jordan Amman 11942 Jordan Nonlinear Dynamics Research Center (NDRC) Ajman University Ajman United Arab Emirates Department of Mathematics Al Zaytoonah University of Jordan Amman 11733 Jordan Applied Mathematics & Modeling Laboratory University of Brothers Mentouri Constantine 25000 Algeria Department of Mathematics Prince Sattam Bin Abdulaziz University Al-Kharj Saudi Arabia Department of Mathematics and Computer Science University of Oum EL-Bouaghi Oum El Bouaghi 04000 Algeria

This study investigates the finite-time stability of fractional-order (FO) discrete Susceptible–Infected–Recovered (SIR) models for COVID-19, incorporating memory effects to capture real-world epidemic dynamics. We use discrete fractional calculus to analyze the stability of disease-free and pandemic equilibrium points. The theoretical framework introduces essential definitions, finite-time stability (FTS) criteria, and novel fractional-order modeling insights. Numerical simulations validate the theoretical results under various parameters, demonstrating the finite-time convergence to equilibrium states. Results highlight the flexibility of FO models in addressing delayed responses and prolonged effects, offering enhanced predictive accuracy over traditional integer-order approaches. This research contributes to the design of effective public health interventions and advances in mathematical epidemiology. © 2025

关键词： Disease-free equilibrium Epidemic modeling Finite-time stability Fractional-order discrete SIR model Pandemic equilibrium

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Laminar chaos in systems with variable delay time 5

Laminar chaos in systems with variable delay time

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5th Scientific School on dynamics of Complex Networks and their Applications, DCNA 2021

作者： Ponomarenko, Vladimir Kulminskiy, Danil Prokhorov, Mikhail Laboratory of Nonlinear Dynamics Modeling Saratov Branch of the Institute of Radio Engineering and Electronics of Russian Academy of Sciences Saratov Russia

ISBN: (纸本)9781665442824

In this paper, we investigated a self-oscillating ring system with variation of the delay time, which demonstrates the phenomenon of laminar chaos. The presence of laminar chaos is demonstrated for various laws of time delay variation - sinusoidal, sawtooth, and triangular. The behavior of coupled systems with laminar chaos and diffusive coupling is investigated. The presence of synchronous behavior is shown. © 2021 IEEE

关键词： Timing circuits

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Using FPGA for developing hybrid system of coupled neuron-like radiophysical oscillators 7

Using FPGA for developing hybrid system of coupled neuron-li...

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7th Scientific School: dynamics of Complex Networks and their Applications, DCNA 2023

作者： Ezhov, Dmitry M. Ponomarenko, Vladimir V. Prokhorov, Mikhail D. Kurbako, Aleksander V. Saratov State University Laboratory of Nonlinear Dynamics Modelling Saratov Branch The Institute of RadioEngineering and Electronics of Russian Academy of Science Department of Dynamic Modeling and Biomedical Engineering Saratov Russia Saratov Branch of the Institute of RadioEngineering and Electronics of Russian Academy of Science Laboratory of Nonlinear Dynamics Modelling Saratov Russia

ISBN: (纸本)9798350305746

We developed and described with Verilog hardware module for implementation configuring coupling between oscillators. We used it to couple radiophysical oscillators FitzHugh-Nagumo. Possibility and prospects of usage FPGA in hybrid analog-digital systems for flexible configuration of couplings between neuron-like oscillators was shown. © 2023 IEEE.

关键词： Hybrid systems

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Role of the Bidirectional Cardiorespiratory Coupling in the nonlinear dynamics of the Cardiovascular System 6

Role of the Bidirectional Cardiorespiratory Coupling in the ...

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6th Scientific School "dynamics of Complex Networks and their Applications", DCNA 2022

作者： Karavaev, Anatoly S. Ishbulatov, Yurii M. Bibicheva, Tatiana S. Gridnev, Vladimir I. Prokhorov, Mikhail D. Ogneva, Marina V. Kiselev, Anton R. Institute of Cardiological Research Saratov State Medical University Laboratory of Nonlinear Dynamics Modelling Saratov Branch The Institute of RadioEngineering and Electronics of Russian Academy of Sciences Saratov State University Research Department Saratov Russia Institute of Cardiological Research Saratov State Medical University Regional Scientific and Educational Mathematical Center of the P.G. Demidov Yaroslavl State University Laboratory of Nonlinear Dynamics Modelling Saratov Branch The Institute of RadioEngineering and Electronics of Russian Academy of Sciences Saratov State University Research Department Saratov Russia Saratov State University Research Department Saratov Russia Institute of Cardiological Research Saratov State Medical University Saratov Russia Laboratory of Nonlinear Dynamics Modeling Saratov Branch The Institute of Radio Engineering and Electronics of Russian Academy of Sciences Saratov State University Research Department Saratov Russia Coordinating Center for Fundamental Research National Medical Research Center for Therapy and Preventive Medicine Russia Saratov Russia

ISBN: (数字)9781665461740

ISBN: (纸本)9781665461740

healthy heart rate is irregular, and numerical measures of its complexity, such as the largest Lyapunov exponent and the correlation dimension, are perspective early markers of cardiovascular diseases. However, the origin of irregularity in the cardiovascular system is still debated, which makes it harder to give the physiological interpretation to the complexity measures. According to a prominent hypothesis, the nonlinear bi-directional cardiovascular coupling could be a source of the complexity, but experimental investigation of this theory is limited by the limitation of modern measuring equipment, nonstationarity of real biological signals, and very strict restrictions on the designs of the active experiments imposed to insure the safety of the subjects. We investigated the role of bidirectional cardiovascular coupling using a mathematical model of cardiovascular system and respiratory systems. We simulated an active experiment with the blockade of the autonomic control of respiration, which disturbed the coupling, and then measured changes in the dynamics of the cardiovascular system using spectral analysis, statistical analysis and complexity measures. © 2022 IEEE.

关键词： Cardiovascular system

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Multi-dimensional detection metrics for automotive three-way catalyst on-board diagnostic monitoring

Multi-dimensional detection metrics for automotive three-way...

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12th IASTED International Conference on Intelligent Systems and Control, ISC 2009

作者： Kirschman, Jill S. Muske, Kenneth R. Jones, James C. Peyton Howse, James W. Center for Nonlinear Dynamics and Control Villanova University Villanova PA 19085 United States Los Alamos National Laboratory Modeling Algorithms and Infomatics Group Los Alamos NM 87545 United States

ISBN: (纸本)9780889868144

An automotive catalyst system health on-board monitor based on multi-dimensional detection metrics is presented in this work. The detection metrics are determined from the real-time measurements available in modern automotive catalytic aftertreatment systems. Preliminary results based on experimental vehicle testing indicate that it is possible to perform accurate discrimination between catalysts of varying health using these metrics.

关键词： Catalysts

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Development of Real-Time Methods for Calculating Cardiointervalograms for Estimating the State of the Cardiovascular System Using a Single Photoplethysmogram Signal 6

Development of Real-Time Methods for Calculating Cardiointer...

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6th Scientific School "dynamics of Complex Networks and their Applications", DCNA 2022

作者： Kurbako, Aleksander V. Skazkina, Victoria V. Borovkova, Ekaterina I. Karavaev, Anatoly S. Saratov State University Laboratory of Nonlinear Dynamics Modelling Saratov Branch The Institute of RadioEngineering and Electronics of Russian Academy of Science Department of Dynamic Modeling and Biomedical Engineering Saratov Russia Institute of Cardiological Research Saratov State Medical University Laboratory of Nonlinear Dynamics Modelling Saratov Branch The Institute of RadioEngineering and Electronics of Russian Academy of Sciences Department of Innovative Cardiological Information Technology Saratov Russia

ISBN: (数字)9781665461740

ISBN: (纸本)9781665461740

We have developed four real-time methods for calculating a cardiointervalogram from a photoplethysmogram signal to calculate the total percentage of phase synchronization for estimating the state of the cardiovascular system. The methods were compared with the classical method of calculating a cardiointervalogram from an electrocardiogram signal using signals recorded from healthy volunteers and patients with COVID-19. © 2022 IEEE.

关键词： Cardiovascular system

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Reconstructions of model equations of time-delay system from short experimental time series

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International Journal of modeling, Simulation, and Scientific Computing 2020年第2期11卷 91-99页

作者： Anatoly S.Karavaev Yurii M.Ishbulatov Ekaterina I.Borovkova Danil D.Kulminskiy Vladimir S.Khorev Anton R.Kiselev Vladimir I.Ponomarenko Vladimir I.Gridnev Mikhail D.Prokhorov Boris P.Bezruchko Department of Dynamic Modeling and Biomedical Engineering Saratov State University 83 Astrakhanskaya Street Saratov410012Russia Laboratory of Nonlinear Dynamics Modeling Saratov Branch of the Institute of Radio Engineering and Electronics of Russian Academy of Sciences 38 Zelyonaya Street Saratov410019Russia Department of New Cardiological Informational Technologies Institute of Cardiological Research Saratov State Medical University 112 Bolshaya Kazachaya StreetSaratov410012Russia

This study aims to investigate the scope of methods for the reconstruction of time-delay *** consider an approach to the reconstruction of time-delay systems based on the synchronous response of the driven system with the structure similar to the structure of the studied *** approach is used for the recovery of the parameters of timedelay systems from short and noisy time *** show the operational performance and capabilities of this approach,the parameters were reconstructed for a radiophysical chaotic generator with quadratic nonlinearity and for the model of a system for the baroreflectory regulation of the mean arterial pressure.

关键词： Time-delay systems reconstruction chaos radiophysical experiment

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