Article
Mathematics, Applied
Priscila F. S. Guedes, Eduardo M. A. M. Mendes, Erivelton Nepomuceno
Summary: This paper introduces a computationally efficient discretization scheme for nonlinear dynamical systems. By neglecting high-order terms in the Runge-Kutta method, computational efficiency is improved without sacrificing accuracy and system characteristics. Experimental results demonstrate the effectiveness and reliability of the proposed scheme for embedded and large-scale applications.
APPLIED MATHEMATICS AND COMPUTATION
(2022)
Article
Physics, Fluids & Plasmas
Johann Maddi, Christophe Coste, Michel Saint Jean
Summary: This study investigates a conservative but nonintegrable dimer system in a periodic potential well and discovers its surprisingly rich dynamics. By employing systematic asymptotic analysis and numerical integration, the amplitude equations for the center of mass motion and relative motion are derived, and reliable estimates of the parameters for autoparametric resonance are provided.
Article
Engineering, Multidisciplinary
Ulrich Gael Ngouabo, Frank Xavier Ngagoum Tchamdjeu
Summary: This study focuses on the study and FPGA implementation of non-linear time-delay equations in dynamic systems. The stability analysis and numerical simulations reveal the oscillation behavior of the systems. A hardware architecture based on the fourth-order Runge-Kutta method is proposed for FPGA implementation, and the results match the numerical simulations.
ALEXANDRIA ENGINEERING JOURNAL
(2022)
Article
Engineering, Mechanical
Alberto Paiva, Rodrigo Veronese Moreira, Alex Brandao, Marcelo A. Savi
Summary: This work investigates the dynamics of a Jeffcott-based rotor-stator system, modeling the contact between them and its impact on system performance. The study classifies the contact between the rotor and stator into three types of motion: no contact, intermittent contact, and full contact, and explores the influence of rotating speed, contact stiffness, and friction coefficient through numerical simulations and parametric analysis.
NONLINEAR DYNAMICS
(2023)
Article
Computer Science, Information Systems
Sara M. Mohamed, Wafaa S. Sayed, Ahmed H. Madian, Ahmed G. Radwan, Lobna A. Said
Summary: This paper extends a memristive chaotic system with transcendental nonlinearities to the fractional-order domain. The chaotic properties of the extended system are validated through bifurcation analysis and spectral entropy. The presented system is employed in the substitution stage of an image encryption algorithm, demonstrating its efficiency through statistical tests, key sensitivity analysis, and resistance to brute force and differential attacks. The proposed system includes reconfigurable coordinate rotation digital computer (CORDIC) and Grunwald-Letnikov (GL) architectures for trigonometric and hyperbolic functions and fractional-order operator implementations, respectively. It achieved a throughput of 0.396 Gbit/s on the Artix-7 FPGA board.
Article
Engineering, Electrical & Electronic
Raul Murillo, Alberto A. Del Barrio, Guillermo Botella, Christian Pilato
Summary: This paper introduces a method of incorporating the posit data type into the high-level synthesis design process to improve the computational accuracy for scientific applications. Evaluations show that using posit arithmetic reduces computation errors and achieves higher accuracy compared to standard floating-point numbers. The paper also proposes a hybrid scheme that utilizes posit numbers in private local memory while the accelerator operates in the traditional floating-point notation.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
(2023)
Article
Mathematics, Applied
Divya D. Joshi, Prashant M. Gade, Sachin Bhalekar
Summary: In this study, we investigate the fractional maps of complex order in one and two dimensions and find that smooth maps tend to exhibit regular behavior while discontinuous or non-differentiable maps may show chaos. Additionally, complex fractional-order maps that exhibit chaos in two dimensions also demonstrate multistability.
Article
Multidisciplinary Sciences
Johannes Werner, Tobias Pietsch, Frank M. Hilker, Hartmut Arndt
Summary: This article discusses the importance of oscillations and deterministic chaos in natural biological systems, particularly in single-species systems. Through experimental and modeling studies, the nonlinear dynamics and deterministic chaos characteristics are discovered in single-species systems of protists in continuous experimental chemostat system. The study also demonstrates the significant influence of complex processes occurring in single cells on the dynamic behavior at the population level.
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
(2022)
Article
Mathematics, Interdisciplinary Applications
Bahaa-Aldeen M. Abo-Alnaga, Lobna A. Said, Ahmed H. Madian, Ahmed G. Radwan
Summary: This paper studies the capability of digital architecture to mimic fractal behavior and achieves fractal behavior by implementing a complex single-dimensional discrete chaotic system, hoping that fractals can be applied in digital applications like chaotic attractors.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Physics, Multidisciplinary
B. Kaviya, R. Gopal, R. Suresh, V. K. Chandrasekar
Summary: We study the dynamics of a damped and driven Mathews-Lakshmanan oscillator type model with position-dependent mass term and find two distinct bifurcation routes leading to sudden, intermittent large-amplitude chaotic oscillations. These infrequent and recurrent large oscillations are characterized as extreme events (EE) when they exceed a pre-defined threshold height. Our findings reveal the emergence of EE from two different bifurcation routes, which has not been reported before. We discuss that EE are caused by the sudden expansion of the chaotic attractor through interior crisis in the system. The different dynamical states are distinguished using Lyapunov exponent spectrum, and the SNA and QP dynamics are determined using singular spectrum analysis and 0-1 test. The region of EE is characterized using the threshold height.
EUROPEAN PHYSICAL JOURNAL PLUS
(2023)
Article
Materials Science, Multidisciplinary
Frank Schindler, Nicolas Regnault, B. Andrei Bernevig
Summary: In this work, a large family of exact eigenstates for density-density interaction terms is found, showing diverse real-space entanglement entropy scaling behaviors and identified through momentum-space entanglement as quantum many-body scars. These exact states differ from typical eigenstates in their momentum-space entanglement and are enabled by the interplay of Fermi statistics and chirality.
Article
Optics
Maxime Martinez, Pierre-Elie Larre, Dominique Delande, Nicolas Cherroret
Summary: In random kicked rotors with local interactions, the system exhibits a rich dynamical phase diagram when the random kinetic energy is smaller than the interaction energy. This includes a low-energy prethermal phase and sharp crossovers towards full thermalization.
Article
Chemistry, Multidisciplinary
Aceng Sambas, Sundarapandian Vaidyanathan, Talal Bonny, Sen Zhang, Sukono, Yuyun Hidayat, Gugun Gundara, Mustafa Mamat
Summary: This paper presents a new mathematical model for a three-dimensional chaotic system and conducts a thorough analysis of its properties. The model is ultimately realized on a Field-Programmable Gate Array (FPGA).
APPLIED SCIENCES-BASEL
(2021)
Article
Engineering, Mechanical
Prasanjit Kumar Kundu, Shyamal Chatterjee
Summary: In this paper, a centralized nonlinear controller is proposed to generate and control self-excited periodic, quasiperiodic, chaotic and hyper-chaotic oscillations in a fully actuated spring-mass-damper mechanical system. The analytical relations among amplitude, frequency and controller parameters have been obtained using the method of two-time scale. Numerical simulations reveal a region of multistability in the plane of control parameters, where system responses can be periodic, quasiperiodic, chaotic or hyper-chaotic depending on initial conditions. The results have potential applications in various macro- and micro-mechanical systems.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics
Omar Guillen-Fernandez, Maria Fernanda Moreno-Lopez, Esteban Tlelo-Cuautle
Summary: Research demonstrates the FPGA implementation of chaotic and hyper-chaotic oscillators, emphasizing the challenges in choosing numerical methods and time-step. Case studies analyze the impact of different numerical methods on the chaotic time series produced by oscillators, as well as the Lyapunov exponents and DKY of the oscillators. Oscillators with higher exponents and DKY are selected for applications in chaotic secure communications.
Article
Engineering, Mechanical
Artur Karimov, Vyacheslav Rybin, Ekaterina Kopets, Timur Karimov, Erivelton Nepomuceno, Denis Butusov
Summary: This article proposes a novel technique for reconstructing ordinary differential equations (ODEs) describing chaotic analog circuits from data. By developing a special system reconstruction algorithm and a synchronization-based technique, the accurate white-box model of the circuit can be obtained. Through a case study, it is found that the reconstructed ODEs have approximately 100 times lower mean synchronization error compared to the original equations.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Burhaneddin Izgi, Murat Ozkaya, Nazim Kemal Ure, Matjaz Perc
Summary: This paper extends and applies the Matrix Norm (MN) approach to nonzero-sum bimatrix games, providing preliminary results for the convergence of the MN approach. The authors introduce a notation for expressing nonzero-sum bimatrix games in terms of two matrix games and prove theorems regarding the boundaries of the game value. They also refine the boundaries for zero/nonzero-sum matrix games, successfully improving the game value interval. The paper demonstrates the consistency of the approaches through various bimatrix game examples.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Engineering, Mechanical
Kaipeng Hu, Zhouhong Li, Lei Shi, Matjaz Perc
Summary: In the rich variety of biological interaction patterns, the state of an individual often does not depend solely on immediate factors but is significantly associated also with interactions or circumstances from the past. In evolutionary game theory, delayed reciprocity is a common phenomenon that affects the evolution of cooperation. This paper studies three different two-species evolutionary models and finds that the type of interaction, whether it's intraspecific or interspecific, as well as the delay period, can have different effects on the stability and convergence of the system.
NONLINEAR DYNAMICS
(2023)
Article
Physics, Multidisciplinary
Maja Duh, Marko Gosak, Matjaz Perc
Summary: In hyperbolic networks, the public goods game is influenced by network mixing and interdependence between networks. It is found that cooperation may have opposite effects in different networks. Optimal conditions for this phenomenon can be determined by considering mixing frequency and network interconnectedness.
Article
Physics, Multidisciplinary
Kaipeng Hu, Lei Shi, Yewei Tao, Matjaz Perc
Summary: The Matthew effect emphasizes the amplification of early advantage over time and its implications for public cooperation are not fully understood. In this study, a spatial public goods game driven by cumulative advantage is proposed and analyzed. Simulation results show that the Matthew effect leads to an irreversible polarization of individual wealth on the network, with moderate levels of cooperation being prevalent, explaining the coexistence of prosocial and antisocial behavior. Heterogeneous networks may restrict the wealth polarization but also inhibit the evolution of cooperation, challenging the commonly held view that they enhance cooperation.
Article
Biology
Sayantan Nag Chowdhury, Jeet Banerjee, Matjaz Perc, Dibakar Ghosh
Summary: Predator-prey interactions are a central research theme in ecology, but the role of parasites in these interactions is often overlooked. Using a predator-prey-parasite model inspired by classical equations, we demonstrate that a stable coexistence of all three species is not biologically realistic. To improve this, we introduce the concept of free space as a relevant eco-evolutionary component in a new mathematical model, which describes a more realistic setup using a game-theoretical payoff matrix. By considering free space, we stabilize the dynamics between the three species through cyclic dominance, determining the parameter regions of coexistence and the types of bifurcations leading to it.
JOURNAL OF THEORETICAL BIOLOGY
(2023)
Article
Mathematics, Applied
Manuel Chica, Juan M. Hernandez, Matjaz Perc
Summary: Tourism, a growing sector globally, is causing sustainability problems in popular destinations due to excessive tourist flows and inappropriate behavior. This paper explores the most efficient strategy for incentivizing sustainable tourism using an asymmetric evolutionary game. The study analyzes the application of rewarding policies to a spatial lattice where tourists and stakeholders interact, and tourists have mobility. Results indicate that an adaptive rewarding strategy, altering the incentive budget over time, is more effective than simple strategies focusing on one sub-population. However, rewarding tourists exclusively becomes the most effective strategy when population density decreases.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Energy & Fuels
Denise Fonseca Resende, Leandro Rodrigues Manso Silva, Erivelton Geraldo Nepomuceno, Carlos Augusto Duque
Summary: This paper presents a method to improve the frequency response of instrument transformers using blind channel equalization and genetic algorithm. The proposed method can compensate for distortions caused by current and voltage transformers without prior knowledge.
Article
Computer Science, Information Systems
Thalita Nazare, Josefredo Gadelha, Erivelton Nepomuceno, Rene Lozi
Summary: The global IT industry accounts for approximately 2% of the world's greenhouse gas emissions, and its energy consumption is projected to increase by 5% annually. Green computing has emerged as a crucial area of research to develop sustainable practices and mitigate the environmental impact of the computing industry.
IEEE LATIN AMERICA TRANSACTIONS
(2023)
Article
Automation & Control Systems
Hao Guo, Zhao Song, Matjaz Perc, Xuelong Li, Zhen Wang
Summary: The conflicts in human societies are often studied using evolutionary games. By developing a two-layer game theoretic framework, we explore how intervention by third parties can influence the evolution of cooperation. We find that intervention can stimulate or inhibit cooperation by weakening or strengthening the dilemma faced by the disputing parties. Furthermore, the outcome in the disputant layer triggered by intervention can in turn stimulate its own evolution, and even a minority of interveners can promote higher levels of cooperation.
IEEE TRANSACTIONS ON SYSTEMS MAN CYBERNETICS-SYSTEMS
(2023)
Article
Multidisciplinary Sciences
Jelena Joksimovic, Matjaz Perc, Zoran Levnajic
Summary: In Slovenia, private companies have received public funding from January 2003 to May 2020. The distribution of money among these companies follows certain patterns, with evidence of a first-mover advantage. The funding received by companies also shows a roughly linear trend over time, indicating the presence of self-organizing principles in Slovenian public spending.
ROYAL SOCIETY OPEN SCIENCE
(2023)
Article
Public, Environmental & Occupational Health
Rene Markovic, Vladimir Grubelnik, Tadej Zavrsnik, Helena Blazun Vosner, Peter Kokol, Matjaz Perc, Marko Marhl, Matej Zavrsnik, Jernej Zavrsnik
Summary: This study aims to uncover different profiles of type 2 diabetes patients based on medication intake records and laboratory measurements. The results show a well-structured profile distribution characterizing different age groups of individuals with diabetes. The middle-aged groups are characterized by several distinct profiles with a wide range of medications associated with the distinct complications of type 2 diabetes.
FRONTIERS IN PUBLIC HEALTH
(2023)
Article
Physics, Fluids & Plasmas
Kaipeng Hu, Pengyue Wang, Junzhou He, Matjaz Perc, Lei Shi
Summary: This study investigates the interactions among individuals in different populations, finding that interactions across multiple populations can promote the evolution of cooperation depending on the level of interaction asymmetry. If interactions within and between populations are symmetric, the presence of multiple populations alone can promote the evolution of cooperation. Asymmetric interactions can further promote cooperation but at the expense of the coexistence of competing strategies.
Article
Physics, Fluids & Plasmas
Shupeng Gao, Lili Chang, Matjaz Perc, Zhen Wang
Summary: The emergence of patterns in nature can be explained mathematically by reaction-diffusion systems, known as Turing patterns. With advances in network science and the study of higher-order interactions, pattern formation in simplicial complexes is of importance. In this study, we show that Turing patterns in simplicial complexes are fundamentally different from traditional networks, with stable distributions and possible emergence only under higher-order interactions.
Article
Physics, Multidisciplinary
Juan Wang, Shiqiang Guo, Chengyi Xia, Matjaz Perc
Summary: Through experiments and simulations, it has been found that increasing the utility coupling between network layers can enhance the level of cooperation, while increasing the number of 2-simplex interactions tends to decrease cooperation. However, despite this result, the overall level of cooperation on interdependent networks is still higher than that on isolated networks.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Bo Li, Tian Huang
Summary: This paper proposes an approximate optimal strategy based on a piecewise parameterization and optimization (PPAO) method for solving optimization problems in stochastic control systems. The method obtains a piecewise parameter control by solving first-order differential equations, which simplifies the control form and ensures a small model error.
CHAOS SOLITONS & FRACTALS
(2024)
Article
Mathematics, Interdisciplinary Applications
Guram Mikaberidze, Sayantan Nag Chowdhury, Alan Hastings, Raissa M. D'Souza
Summary: This study explores the collective behavior of interacting entities, focusing on the co-evolution of diverse mobile agents in a heterogeneous environment network. Increasing agent density, introducing heterogeneity, and designing the network structure intelligently can promote agent cohesion.
CHAOS SOLITONS & FRACTALS
(2024)
Article
Mathematics, Interdisciplinary Applications
Gengxiang Wang, Yang Liu, Caishan Liu
Summary: This investigation studies the impact behavior of a contact body in a fluidic environment. A dissipated coefficient is introduced to describe the energy dissipation caused by hydrodynamic forces. A new fluid damping factor is derived to depict the coupling between liquid and solid, as well as the coupling between solid and solid. A new coefficient of restitution (CoR) is proposed to determine the actual physical impact. A new contact force model with a fluid damping factor tailored for immersed collision events is proposed.
CHAOS SOLITONS & FRACTALS
(2024)
