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On fractional discrete financial system:Bifurcation,chaos,and control

Chinese Physics B 2024年第10期33卷 129-140页

作者： Louiza Diabi Adel Ouannas Amel Hioual Shaher Momani Abderrahmane Abbes Laboratory of Dynamical Systems and Control University of Larbi Ben M’hidiOum El Bouaghi 04000Algeria Department of Mathematics and Computer Science University of Larbi Ben M’hidiOum El Bouaghi 04000Algeria Nonlinear Dynamics Research Center Ajman UniversityAjman 346United Arab Emirates Department of Mathematics The University of JordanAmman 11942Jordan Laboratory of Mathematics Dynamics and ModelizationUniversity Badji MokhtarAnnaba 23000Algeria

The dynamic analysis of financial systems is a developing field that combines mathematics and economics to understand and explain fluctuations in financial *** paper introduces a new three-dimensional(3D)fractional financial map and we dissect its nonlinear dynamics system under commensurate and incommensurate *** such,we evaluate when the equilibrium points are stable or unstable at various fractional *** use many numerical methods,phase plots in 2D and 3D projections,bifurcation diagrams and the maximum Lyapunov *** techniques reveal that financial maps exhibit chaotic attractor *** study is grounded on the Caputo-like discrete operator,which is specifically influenced by the variance of the commensurate and incommensurate ***,we confirm the presence and measure the complexity of chaos in financial maps by the 0-1 test and the approximate entropy ***,we offer nonlinear-type controllers to stabilize the fractional financial *** numerical results of this study are obtained using MATLAB.

关键词： financial model stability chaos commensurate and incommensurate orders complexity

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Design of unbiased reduced order filter for stochastic systems with sampled measurements 12

Design of unbiased reduced order filter for stochastic syste...

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12th International Conference on Mathematical Modeling in Physical sciences, IC-MSQUARE 2023

作者： Kamenshchikov, Mikhail Lomonosov Moscow State University Faculty of Computational Mathematics and Cybernetics Department of Nonlinear Dynamical Systems and Control Processes Moscow119991 Russia V. A. Trapeznikov Institute of Control Sciences Russian Academy of Sciences Laboratory of Terminal Control Systems Moscow117997 Russia National University of Science and Technology "MISiS" Department of Engineering Cybernetics Moscow119049 Russia

The problem of synthesizing reduced order filter, that forms an unbiased estimate of linear functional from an unknown phase vector of a continuous time stochastic system with sampled measurements and additive noises, is considered in this work. The H2 norm of the weighted transfer function from input noises to estimation error is used as a performance criterion. The method for reduced order filter design is based on the expression of the explicit dependence of performance criterion on unknown parameters in the canonical basis and the application of the non-convex optimization technique. Numerical simulations are performed to illustrate the proposed approach. © 2024 Institute of Physics Publishing. All rights reserved.

关键词： Stochastic systems

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Finite-Time Stability of ABC Type ℏ-Fractional Discrete Neural Networks: Gronwall Inequality and Stability Criterion

Finite-Time Stability of ABC Type ℏ-Fractional Discrete Neu...

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2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023

作者： Hioual, Amel Ouannas, Adel Momani, Shaher Oussaeif, Taki-Eddine University of Oum EL-Bouaghi Laboratory of Dynamical Systems and Control Algeria University of Oum EL-Bouaghi Department of Mathematics and Computer Science Algeria Ajman346 United Arab Emirates The University of Jordan Department of Mathematics Amman Jordan

ISBN: (纸本)9798350321685

The dynamics of fractional-order difference neural networks are currently a major research area, with several noteworthy discoveries. The dynamics of discrete-time neural networks with -fractional nonlocal and nonsingular kernels, on the other hand, have not been thoroughly researched, and this paper is one of the first to address this subject. The main focus of this research is the finite-time stability of discrete-time neural networks based on the nabla ABC fractional difference operator. First, the Atangana-Baleanu -fractional difference sum operator is used to investigate a generalized -Gronwall inequality. This inequality also yields the uniqueness theorem and the finite-time stability criterion of nonlinear -fractional neural networks. Finally, several examples are offered to show the effectiveness of our theoretical conclusion. © 2023 IEEE.

关键词： Stability criteria

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Coverage Path Planning with Constraints on Normal Curvature for a Three-dimensional Terrain with Obstacles 16

Coverage Path Planning with Constraints on Normal Curvature ...

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16th International Conference on Stability and Oscillations of Nonlinear control systems (Pyatnitskiy's Conference), STAB 2022

作者： Tormagov, Timofey Rapoport, Lev Skolkovo Institute of Science and Technology Moscow Institute of Physics and Technology Moscow Russia V.A. Trapeznikov Institute of Control Sciences of RAS Laboratory of Nonlinear Dynamical Systems Moscow Russia

ISBN: (纸本)9781665465861

In precision agriculture, the problem of constructing covering paths often appears. It consists in planning some route for an agricultural machine that allows to process field without skipping. Nearly parallel paths are often used for this purpose. If a field is processed by a machine with front wheels steering, then the rear axle center should follow the trajectory with limited normal curvature. Threshold value of normal curvature is determined by the characteristics of the machine. In addition, we must take into account the location of obstacles in the field. In this paper the complete coverage path planning method based on convex optimization is proposed. © 2022 IEEE.

关键词： Second-order cone programming

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control of chaos in incommensurate fractional order discrete system

Control of chaos in incommensurate fractional order discrete...

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2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023

作者： Batiha, Iqbal M. Djenina, Noureddine Ouannas, Adel Oussaeif, Taki-Eddine Aoua, Leila Ben Momani, Shaher Al Zaytoonah University of Jordan Department of Mathematics Amman Jordan Ajman United Arab Emirates University of Larbi Ben m'Hidi Laboratory of Dynamical Systems and Control Oum El Bouaghi Algeria University of Oum EL-Bouaghi Department of Mathematics and Computer Science Oum El Bouaghi Algeria University of Larbi Ben m'Hidi Department of Mathematics and Computer Science Oum El Bouaghi Algeria

ISBN: (纸本)9798350321685

The mathematical study of the growth of a cancer tumor gives us great progress in knowing the behavior of the cancer tumor as well as taking appropriate therapeutic measures. In this article, we endeavor to investigate a mathematical model of a cancer tumor and study its stabilization. In particular, we first discritize the continuous model connected with the dynamics of cancer tumor to get the discrete model. Then we perform several numerical simulations that will show that the proposed discrete model can behave chaotically. As a result, we study the unique fixed point stability that has a physical meaning, and finally we controlled the proposed system to stabilized its dynamics at such a point. © 2023 IEEE.

关键词： Tumors

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Multidimensional Opinion Dynamics with Heterogeneous Bounded Confidences and Random Interactions

arXiv

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arXiv 2024年

作者： Cheng, Jiangjiang Chen, Ge Mei, Wenjun Bullo, Francesco School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China Key Laboratory of Systems and Control Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Department of Mechanics and Engineering Science Peking University Beijing100871 China Department of Mechanical Engineering The Center of Control Dynamical-Systems and Computation University of California Santa BarbaraCA93106-5070 United States

This paper introduces a heterogeneous multidimensional bounded confidence (BC) opinion dynamics with random pairwise interactions, whereby each pair of agents accesses each other’s opinions with a specific probability. This revised model is motivated by the observation that the standard Hegselmann-Krause (HK) dynamics requires unrealistic all-to-all interactions at certain configurations. For this randomized BC opinion dynamics, regardless of initial opinions and positive confidence bounds, we show that the agents’ states converge to fixed final opinions in finite time almost surely and that the convergence rate follows a negative exponential distribution in mean square. Furthermore, we establish sufficient conditions for the heterogeneous BC opinion dynamics with random interactions to achieve consensus in finite time. Copyright © 2024, The Authors. All rights reserved.

关键词： Random processes

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Chaotic Attractors in Quadratic Discrete Tinkerbell System With Non-Commensurate Fractional Variable-Orders: Complexity, Chaos and Entropy∗

Chaotic Attractors in Quadratic Discrete Tinkerbell System W...

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2023 International Conference on Fractional Differentiation and Its Applications, ICFDA 2023

作者： Ahmed, Souad Bensid Ouannas, Adel Horani, Mohammed Al Khennaoui, Amina Aicha Batiha, Iqbal M. The University of Jordan Department of Mathematics Amman Jordan The University of Oum El Bouaghi Department of Mathematics and Computer Science Oum El Bouaghi Algeria The University of Oum El Bouaghi Department Laboratory of Dynamical Systems and Control Oum El Bouaghi Algeria Al Zaytoonah University of Jordan Department of Mathematics Amman Jordan Ajman University Nonlinear Dynamics Research Center Ajman United Arab Emirates

ISBN: (纸本)9798350321685

This manuscript analyzes the dynamical properties of the incommensurate variable fractional discrete Tinkerbell system. Through time evolution of the states, phase portraits, lyapunov exponents and bifurcation diagrams, it is indicated that the two dimensional incommensurate fractional variable-order Tinkerbell map with discrete time exhibits chaotic and periodic behaviour. The approximation entropy is also used to estimate the complexity of the incommensurate variable fractional-order Tinkerbell system with discrete time. Finally, the 0-1 test plots of the presented discrete Tinkerbell map with incommensurate variable fractional-order validate the findings from the largest lyapunov exponents, bifurcation diagrams and approximate entropy. Numerical results are provided out to simulate the effectiveness of the approach described herein. © 2023 IEEE.

关键词： Entropy

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Fractional discrete neural networks with variable order: solvability, finite time stability and synchronization

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The European Physical Journal Special Topics 2024年 1-14页

作者： Hioual, Amel Alomari, Saleh Al-Tarawneh, Hassan Ouannas, Adel Grassi, Giuseppe Laboratory of Dynamical Systems and Control University of Oum El-Bouaghi Oum El Bouaghi Algeria Faculty of Science and Information Technology Software Engineering Jadara University Irbid Jordan Department of Data Sciences and Artificial Intelligence Al-Ahliyya Amman University Amman Jordan Department of Mathematics and Computer Science University of Oum EL-Bouaghi Oum El Bouaghi Algeria Dipartimento Ingegneria Innovazione Universita del Salento Lecce Italy

Research in the field of dynamic behaviors in neural networks with variable-order differences is currently a thriving area, marked by various significant discoveries. However, when it comes to discrete-time neural networks featuring fractional variable-order nonlocal and nonsingular kernels, there has been limited exploration. This paper stands as one of the initial contributions to this subject, focusing primarily on the topics of stability and synchronization in finite-time within discrete neural networks. The research employs the nabla ABC variable-order difference operator, with a primary approach involving the investigation of a novel Gronwall inequality using the Atangana-Baleanu difference variable-order sum operator. This analysis leads to the development of a uniqueness theorem and a criterion for the stability in finite-time of variable-order discrete neural networks. Furthermore, the requirements stemming from this type of stability and the novel Gronwall inequality serve as the foundation for establishing the conditions necessary for achieving finite-time synchronization in these networks, employing a specific control using state feedback method. Finally, the study utilizes numerical solutions to validate the obtained results.

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Finite-Time Stability of ABC Type ℏ-Fractional Discrete Neural Networks: Gronwall Inequality and Stability Criterion

Finite-Time Stability of ABC Type ℏ-Fractional Discrete Neu...

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International Conference on Fractional Differentiation and Its Applications (ICFDA)

作者： Amel Hioual Adel Ouannas Shaher Momani Taki-Eddine Oussaeif Laboratory of Dynamical Systems and Control University of Oum EL-Bouaghi Algeria Department of Mathematics and Computer Science University of Oum EL-Bouaghi Algeria Nonlinear Dynamics Research Center (NDRC) Ajman University Ajman UAE Department of Mathematics The University of Jordan Amman Jordan

The dynamics of fractional-order difference neural networks are currently a major research area, with several noteworthy discoveries. The dynamics of discrete-time neural networks with $\hbar$-fractional nonlocal and nonsingular kernels, on the other hand, have not been thoroughly researched, and this paper is one of the first to address this subject. The main focus of this research is the finite-time stability of discrete-time neural networks based on the nabla ABC fractional difference operator. First, the Atangana-Baleanu $\hbar$-fractional difference sum operator is used to investigate a generalized $\hbar$-Gronwall inequality. This inequality also yields the uniqueness theorem and the finite-time stability criterion of nonlinear $\hbar$-fractional neural networks. Finally, several examples are offered to show the effectiveness of our theoretical conclusion.

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Convergence, Consensus and Dissensus in the Weighted-Median Opinion Dynamics

arXiv

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arXiv 2022年

作者： Mei, Wenjun Hendrickx, Julien M. Chen, Ge Bullo, Francesco Dörfler, Florian The Department of Mechanics and Engineering Science Peking University China The Institute of Information and Communication Technologies Electronics and Applied Mathematics UCLouvain Belgium The Academy of Mathematics and Systems Science Chinese Academy of Sciences China The Center of Control Dynamical-Systems and Computation University of California Santa Barbara United States Automatic Control Laboratory ETH Zurich Switzerland

Mechanistic and tractable mathematical models play a key role in understanding how social influence shapes public opinions. Recently, a weighted-median mechanism has been proposed as a new micro-foundation of opinion dynamics and validated via experimental data. Numerical studies also indicate that this new mechanism recreates some non-trivial real-world features of opinion evolution. In this paper, we conduct a thorough theoretical analysis of the weighted-median opinion dynamics. We fully characterize the set of all equilibria, and we establish the almost-sure finite-time convergence for any initial condition. Moreover, we prove a necessary and sufficient graph-theoretic condition for the almost-sure convergence to consensus, as well as a sufficient graph-theoretic condition for almost-sure persistent dissensus. It turns out that the weighted-median opinion dynamics, despite its simplicity in form, exhibit rich dynamical behavior that depends on some delicate network structures. To complement our sufficient conditions for almost-sure dissensus, we further prove that, given the influence network, determining whether the system almost surely achieves persistent dissensus is NP-hard, which reflects the complexity the network topology contributes to opinion *** Codes 93E03, 93A30, 91D30 Copyright © 2022, The Authors. All rights reserved.

关键词： Network topology

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