Chaos最新文献 - Book学术

Slow passage through a saddle-node bifurcation in discrete dynamical systems. 离散动力系统中鞍节点分岔的缓慢通过。

IF 2.7 2区数学

Chaos Pub Date : 2025-07-01 DOI: 10.1063/5.0242626

Je-Chiang Tsai, Jay Chu, Jun-Jie Lin

{"title":"Slow passage through a saddle-node bifurcation in discrete dynamical systems.","authors":"Je-Chiang Tsai, Jay Chu, Jun-Jie Lin","doi":"10.1063/5.0242626","DOIUrl":"https://doi.org/10.1063/5.0242626","url":null,"abstract":"We study a discrete non-autonomous system whose autonomous counterpart (with the frozen bifurcation parameter) admits a saddle-node bifurcation in which the bifurcation parameter slowly changes in time and is characterized by a sweep rate constant ϵ. The discrete system is more appropriate for modeling realistic systems since only time series data are available. In contrast to its autonomous counterpart, we show that when the ratio ϵ/Δt is of the order O(1), there is a bifurcation delay as the bifurcation time-varying parameter varies through the bifurcation point. The delay is proportional to the two-thirds power of the sweep rate constant ϵ. This bifurcation delay is significant in various realistic systems since it allows one to take necessary action promptly before a sudden collapse or shift to different states. On the other hand, when the ratio ϵ/Δt is of the order o(1), the dynamical behavior of the system is dramatically changed before the bifurcation point. This behavior is not observed in the system's (continuous) autonomous counterpart. Therefore, the system's dynamical behavior strongly depends on the time mesh size, and the ratio ϵ/Δt can be viewed as a measurement of how much extent the system behaves like a discrete system. Finally, the inherently discrete nature of the system significantly increases the complexity of its analytical study. Our approach employs the construction of super- and sub-solutions, complemented by a careful phase portrait analysis, to investigate bifurcation delay phenomena.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 7","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144697753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Bifurcation analysis in a Beddington-DeAngelis predator-prey model with habitat complexity and additional food effect. 具有栖息地复杂性和附加食物效应的Beddington-DeAngelis捕食-食饵模型的分岔分析。

IF 2.7 2区数学

Chaos Pub Date : 2025-07-01 DOI: 10.1063/5.0266107

Demou Luo, Qiru Wang, Huayou Xie, Zhuming Zhang

引用次数: 0

A three-dimensional memristor-based hyperchaotic map for pseudorandom number generation and multi-image encryption. 用于伪随机数生成和多图像加密的三维记忆电阻超混沌映射。

IF 2.7 2区数学

Chaos Pub Date : 2025-07-01 DOI: 10.1063/5.0270220

Suo Gao, Siqi Ding, Herbert Ho-Ching Iu, Uğur Erkan, Abdurrahim Toktas, Cemaleddin Simsek, Rui Wu, Xianying Xu, Yinghong Cao, Jun Mou

{"title":"A three-dimensional memristor-based hyperchaotic map for pseudorandom number generation and multi-image encryption.","authors":"Suo Gao, Siqi Ding, Herbert Ho-Ching Iu, Uğur Erkan, Abdurrahim Toktas, Cemaleddin Simsek, Rui Wu, Xianying Xu, Yinghong Cao, Jun Mou","doi":"10.1063/5.0270220","DOIUrl":"https://doi.org/10.1063/5.0270220","url":null,"abstract":"The resistance state of a memristor can be influenced by external stimuli, and these variations can be converted into a pseudorandom sequence through appropriate circuitry and control mechanisms. By leveraging this property, a reliable and complex pseudorandom number generator suitable for encryption can be designed. To enhance the chaotic complexity of memristor-based discrete systems, this paper introduces a three-dimensional hyperchaotic map based on a memristor (3D-HMBM), which integrates a sine-function nonlinearity with a discrete memristor model. Analyzing its dynamical properties via Lyapunov exponents, the 3D-HMBM exhibits evolution from periodicity to chaos and hyperchaos. The complexity of its iterated sequences is verified through metrics such as Spectral Entropy and C0 complexity. Furthermore, the 3D-HMBM displays a unique phenomenon of infinite coexisting attractors. As initial values vary, the system generates attractors at different positions, suggesting that-in theory-an infinite number of attractors exist. Finally, the simulation results are validated via digital-circuit implementation. Building on this foundation, we propose a multi-image encryption algorithm based on the 3D-HMBM, offering a more secure solution for encrypting large volumes of data. Through statistical testing and cryptographic analysis, we confirm the significant potential of the keystream generated by the 3D-HMBM for cryptographic applications.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 7","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144539160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Liquid dynamics in a crowded environment: Bond percolation vs site percolation. 拥挤环境中的液体动力学：键渗透与点渗透。

IF 2.7 2区数学

Chaos Pub Date : 2025-07-01 DOI: 10.1063/5.0242848

Piotr Polanowski, Andrzej Sikorski

{"title":"Liquid dynamics in a crowded environment: Bond percolation vs site percolation.","authors":"Piotr Polanowski, Andrzej Sikorski","doi":"10.1063/5.0242848","DOIUrl":"https://doi.org/10.1063/5.0242848","url":null,"abstract":"The main problem studied is how the diffusion of liquid occurs in the presence of obstacles. In general, this question cannot be reduced to either bond or site percolation, because in real media, the diffusion problem is a complex combination of bond and site percolation. In this work, we make a comparison between site and bond percolation, where the motion of the elements is closely correlated, which is made possible by the unique properties of the dynamic lattice liquid algorithm (no other method allows this). It is clear that even at the two extremes, it is impossible to reduce the problem to just one type of percolation. It should be emphasized that the above comparison has been made within the framework of a single model, which seems very difficult to do with other methods. Extensive and systematic computer simulations have been carried out on a dense (completely filled system) athermal two-dimensional liquid model on a triangular lattice. The behavior of all investigated parameters clearly shows that, for the same obstacle concentration, the liquid molecules in the model with blocked sites are much more mobile, especially as the probability of blocking or the obstacle concentration increases. The research presented here shows that the dynamics of the system is closely related to the morphology of the system. What matters is not only the absolute number of obstacles but the detailed morphology of the local distribution of obstacles and bonds (channels) of the systems.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 7","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144539165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Rate-induced phenomena in dynamical systems with attracting limit cycles. 具有吸引极限环的动力系统中的速率诱导现象。

IF 2.7 2区数学

Chaos Pub Date : 2025-07-01 DOI: 10.1063/5.0251098

George Chappelle, Martin Rasmussen

引用次数: 0

Physics informed neural networks simulation of fingering instabilities arising during immiscible and miscible multiphase flow in oil recovery processes. 基于物理的神经网络模拟了采油过程中非混相和混相多相流的指进不稳定性。

IF 2.7 2区数学

Chaos Pub Date : 2025-07-01 DOI: 10.1063/5.0273935

Pavan Patel, Saroj R Yadav

{"title":"Physics informed neural networks simulation of fingering instabilities arising during immiscible and miscible multiphase flow in oil recovery processes.","authors":"Pavan Patel, Saroj R Yadav","doi":"10.1063/5.0273935","DOIUrl":"https://doi.org/10.1063/5.0273935","url":null,"abstract":"Numerical simulation and experimental techniques are the primary methods for solving fluid dynamics problems. However, while numerical simulation approaches are sensitive when meshing a complex structure, experimental methods have difficulty simulating the physical challenges. Therefore, building an affordable model to solve the fluid dynamics problem is very important. Deep learning (DL) approaches have great abilities to handle strong nonlinearity and high dimensionality that attract much attention for solving fluid dynamics problems. In this paper, we used a deep learning-based framework, physics-informed neural networks (PINNs). The main idea of PINN approaches is to encode the underlying physical law (i.e., the partial differential equation) into the neural network as prior information. In the oil recovery process involving the injection of fluids and multiphase flow in porous media, fingering instability is observed if a fluid with low viscosity displaces a high viscosity fluid. This paper provides a deep learning framework to simulate the instability (fingering) phenomenon during secondary and enhanced oil recovery methods. We have considered two models, namely, the first model on immiscible multiphase flow from the secondary oil recovery method, which is analyzed both with and without deliberating mass flow rate. In the second model, instability arising during the enhanced oil recovery method involving miscible displacement of multiphase is examined, focusing on oil recovery using carbonated water injection. We solve the governing nonlinear partial differential equation using PINNs. Furthermore, we have compared results from PINNs with the semi-analytical solution from the literature. The results show that PINNs are very effective in fluid flow problems and deserve further research.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 7","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144599539","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Synchronization of spring pendula. 弹簧摆的同步。

IF 2.7 2区数学

Chaos Pub Date : 2025-07-01 DOI: 10.1063/5.0282572

Dawid Dudkowski, Tomasz Kapitaniak

引用次数: 0

Switching-induced bifurcation analysis for piecewise nonlinear dynamical systems: A semi-analytical approach. 分段非线性动力系统的开关诱导分岔分析：一种半解析方法。

IF 2.7 2区数学

Chaos Pub Date : 2025-07-01 DOI: 10.1063/5.0243774

Kai Jiang, Jianzhe Huang, Xilin Fu

{"title":"Switching-induced bifurcation analysis for piecewise nonlinear dynamical systems: A semi-analytical approach.","authors":"Kai Jiang, Jianzhe Huang, Xilin Fu","doi":"10.1063/5.0243774","DOIUrl":"https://doi.org/10.1063/5.0243774","url":null,"abstract":"In piecewise nonlinear dynamical systems, the flow is governed by different vector fields across discontinuous boundaries. When switching occurs at these boundaries, the governing vector field changes, inevitably causing the steady-state response to retain transient dynamics from individual subsystems. However, obtaining a complete analytical solution-including the transient component-for each nonlinear subsystem remains an unresolved challenge. This presents significant obstacles to finding unstable hidden bifurcation routes in such systems. The main objective of this paper is to obtain the complete bifurcation trees for piecewise nonlinear dynamical systems, enabling a comprehensive analysis of unconventional bifurcations induced by flow switching. A semi-analytical framework is proposed which integrates generalized mapping structures with local singularity theory to systematically characterize flow-switching dynamics at discontinuous boundaries. A generalized mapping formalism with closed-form constraint conditions at switching points is developed to parameterize periodic motions with higher-order singularities. To demonstrate the effectiveness of the proposed method, we analyze a piecewise nonlinear memristor circuit system exhibiting complex bifurcation and chaotic behaviors. This approach can be readily extended to study other piecewise nonlinear systems.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 7","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144697754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Reset induced multimodality in unbounded potential. 无界电位中复位诱导的多模态。

IF 2.7 2区数学

Chaos Pub Date : 2025-07-01 DOI: 10.1063/5.0274016

Karol Capała

引用次数: 0

Wavelet-based coarse graining for percolation criticality from a single system size. 基于小波的粗粒化从单一系统尺寸的渗透临界。

IF 2.7 2区数学

Chaos Pub Date : 2025-07-01 DOI: 10.1063/5.0276783

Soo Min Oh, Brani Vidakovic

{"title":"Wavelet-based coarse graining for percolation criticality from a single system size.","authors":"Soo Min Oh, Brani Vidakovic","doi":"10.1063/5.0276783","DOIUrl":"https://doi.org/10.1063/5.0276783","url":null,"abstract":"Scaling analysis is a fundamental tool for estimating critical points and exponents of phase transitions in complex systems, typically relying on numerical simulations at multiple system sizes or scales. However, real-world systems often exist at a single system size, making such analysis challenging. Here, we propose a wavelet-based method to extract scaling behavior from a single system size. Considering two-dimensional random and explosive site percolation, we perform wavelet-based coarse graining and compute high-frequency coefficients across multiple effective system sizes, each of which corresponds to the size of the transformed system at a coarser resolution. In these coarser systems, wavelet energy is defined as the squared coefficients that capture cluster boundaries. We finally demonstrate that average wavelet energies follow a scaling law, enabling accurate estimation of the critical points and exponents, which are consistent with those obtained from traditional susceptibility-based scaling analysis. This suggests that average wavelet energy serves as a susceptibility-like observable in percolation systems. Our findings highlight that wavelet-based analysis provides a new perspective on percolation criticality, allowing the identification of scaling properties from a single system size. Furthermore, this approach is potentially applicable to real-world systems such as brain activity patterns, bacterial colonies, or social networks, where collecting data at multiple sizes is impractical or costly.","PeriodicalId":9974,"journal":{"name":"Chaos","volume":"35 7","pages":""},"PeriodicalIF":2.7,"publicationDate":"2025-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144583224","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0