Communications in Nonlinear Science and Numerical Simulation最新文献

{"title":"On the inverse scattering transform problem for the modified intermediate long wave equation: Deep- and shallow-water limits","authors":"Ning Guo","doi":"10.1016/j.cnsns.2025.109099","DOIUrl":"10.1016/j.cnsns.2025.109099","url":null,"abstract":"<div><div>We study the initial value problem for the modified intermediate long wave (mILW) equation on the real line via the inverse scattering transform method and then analyze its scattering behavior in deep- and shallow-water limits. We show that the symmetry property of eigenfunctions reduces nonlocal and the transmission coefficient <span><math><mrow><mi>a</mi><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></math></span> normalized in the deep-water limit, revealing the fundamental difference between the mILW and modified Benjamin–Ono equations’ direct scattering problem. We also show that the Lax pair of the mILW equation reduces to a second-order modified Korteweg–de Vries spectral problem in the shallow water limit. This reduction adds additional scattering properties to the Jost solution, providing an analytical framework for breather and weak-bound state solutions. The inverse problem for these equations is then characterized by the scalar Riemann–Hilbert problem, with solitons and exceptional cases in the reflectionless case further analyzed.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109099"},"PeriodicalIF":3.4,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655112","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}

{"title":"Identification of important nodes in complex networks based on node and edge information","authors":"Wenjing Sun,&nbsp;Chunjiang Lan,&nbsp;Cheng Yang,&nbsp;Wenlin Pan","doi":"10.1016/j.cnsns.2025.109116","DOIUrl":"10.1016/j.cnsns.2025.109116","url":null,"abstract":"<div><div>Aiming at the previous definition of important nodes, important nodes are redefined from the perspective of resource allocation and a new algorithm of identifying important nodes, DSE (Effective Distance-Structural Hole-Edges), is proposed. This algorithm utilizes the effective distance to represent the resource allocation, combines the number of ”holes” (i.e., the number of intermediary positions) and the importance of edges (where the K-shell algorithm is extended from identifying nodes to identifying edges). The performance of DSE and six commonly used centrality indicators in identifying important nodes is analyzed by using the SIR model simulation experiments in the nine real networks and the constructed networks. Finally, the feasibility of DSE algorithm is analyzed by using the Kendall’s tau correlation coefficient and the M(R) index. The experimental results show that the top-1% nodes and top-5% nodes identified by DSE have almost the highest ability to infect nodes in both the nine networks and the constructed networks. Additionally, the Kendall’s tau correlation coefficients are all positively correlated, and the M(R) values are all above 0.99. These show that the definition of important nodes in this paper is realistic and the DSE algorithm can effectively evaluate the importance of nodes.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109116"},"PeriodicalIF":3.4,"publicationDate":"2025-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655116","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}

{"title":"Exploring cost-effectiveness analysis in delayed optimal control and complex dynamics of an epidemic model with media coverage","authors":"Mst Sebi Khatun,&nbsp;Palakshi Paul,&nbsp;Pritha Das","doi":"10.1016/j.cnsns.2025.109109","DOIUrl":"10.1016/j.cnsns.2025.109109","url":null,"abstract":"&lt;div&gt;&lt;div&gt;This article examines the &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;u&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;S&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mi&gt;a&lt;/mi&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mi&gt;I&lt;/mi&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;mi&gt;M&lt;/mi&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; epidemic model, analyzing both delayed and non-delayed scenarios. This model incorporates linear and nonlinear incidence functions, an incubation delay, and a treatment function dependent on hospital bed availability to explore disease dynamics and associated control factors. In the non-delayed system, to find influential factors for controlling the spread of disease, the local sensitivity of the basic reproduction number &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; is analyzed using the normalized forward sensitivity index method, and the global sensitivity of the infected population is discussed using the LHS-PRCC method. This study includes delayed treatment and media response as controlling parameters within the optimization framework, offering a more realistic and accurate description of dynamics with practical interventions. This work highlights the following key findings: (i) In the non-delayed system, PRCC-LHS analysis reveals that the model outputs exhibit greater variability and identify more significant parameters under a uniform distribution compared to a normal distribution. The backward and transcritical bifurcations at &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;, along with the saddle–node bifurcation related to the transmission rate and the Hopf bifurcation are observed. High values of proper treatment, media efforts, hospital beds, and vaccine coverage are observed to help eliminate the backward bifurcation, making the system disease-free for &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msub&gt;&lt;mrow&gt;&lt;mi&gt;R&lt;/mi&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mn&gt;0&lt;/mn&gt;&lt;/mrow&gt;&lt;/msub&gt;&lt;mo&gt;&lt;&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;. In addition, multiple stability switches are found as a result of a Hopf-Hopf bifurcation caused by the transmission rate, hospital beds, and the rate of unoccupied beds. (ii) In the delayed system, the contour plots reveal that increasing the delay parameter raises the infection levels. Increasing delay values drive frequent stability switches through the Hopf-Hopf bifurcation and lead to the emergence of chaotic dynamics. Despite chaotic behavior caused by a high delay value, increased availability of hospital bed, vaccination, proper treatment, and media coverage have been shown to effectively stabilize the system and control chaotic dynamics. The numerical results of optimal control reveal that implementing all control measures is the most effective in minimizing infection spread, while combining vaccination with proper treatment emerges as the most cost-effective approach. The numerical results further illustrate the enhanced effectiveness of delayed optimal control compared to the non-delayed contro","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109109"},"PeriodicalIF":3.4,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655148","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}

{"title":"Influence of fear and Allee effects on stability and species survival in a tri-trophic food chain","authors":"Vinay Kumar ,&nbsp;Suneel Kumar Bairwa ,&nbsp;Tanvi","doi":"10.1016/j.cnsns.2025.109115","DOIUrl":"10.1016/j.cnsns.2025.109115","url":null,"abstract":"<div><div>This study investigates the impact of fear and Allee effects on the qualitative behavior of a tri-trophic food chain model. We formulate a mathematical model where the fear effect influences the bottom prey population while the top predator is subject to the Allee effect. We establish conditions for the boundedness and persistence of the model. The existence and stability of equilibrium points are analyzed. Comprehensive numerical simulations are performed to verify the analytical findings. Our study reveals that fear and Allee effects significantly impact stability and chaos within the system. In the absence of the Allee effect, the system exhibits more complex dynamics and a broader stability range concerning the strength of the fear effect. Conversely, the presence of the Allee effect, coupled with increased fear strength, leads to a steep decline in the top predator population. The interplay between fear and Allee effects promotes the coexistence and long-term survival of the three species within the system.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109115"},"PeriodicalIF":3.4,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144655208","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}

{"title":"Probabilistic impulsive effects and finite-time synchronization of fuzzy multiplicative stochastic coupled memristive neural networks","authors":"Nijing Yang ,&nbsp;Jia Liu ,&nbsp;Xiang Lu ,&nbsp;Hong Peng ,&nbsp;Xiangxiang Wang ,&nbsp;Yongbin Yu","doi":"10.1016/j.cnsns.2025.109130","DOIUrl":"10.1016/j.cnsns.2025.109130","url":null,"abstract":"<div><div>This paper investigates the finite-time synchronization (FTS) of Takagi–Sugeno (T–S) fuzzy multiplicative stochastic coupled memristive neural networks (CMNNs) with probabilistic delayed impulsive effects. Initially, a novel CMNNs model is developed, incorporating mismatched parameters and adjustable coupling strength to enhance the accuracy of the CMNNs. Multiplicative noise is unavoidable in information transmission. Therefore, this type of noise is taken into account in the CMNNs. To enhance the system’s robustness, a probabilistic time delayed impulsive controller with fuzzy impulsive strength is introduced. Moreover, finite-time stability theory and impulsive control theory are utilized to establish sufficient conditions for FTS with synchronizing and desynchronizing impulses on CMNNs. Meanwhile, the upper bounds for the settling time of synchronization are effectively estimated. Finally, a numerical example is provided to illustrate the effectiveness of the main results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109130"},"PeriodicalIF":3.4,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144665112","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}

{"title":"Novel finite-time convergent neural dynamics for practical synchronization of diverse chaotic systems","authors":"Linyan Dai ,&nbsp;Zhi Liu ,&nbsp;Hanyi Xu ,&nbsp;Yinyan Zhang","doi":"10.1016/j.cnsns.2025.109122","DOIUrl":"10.1016/j.cnsns.2025.109122","url":null,"abstract":"<div><div>The synchronization of chaotic systems with finite-time convergence in noisy environment is a challenging problem. Most existing zeroing neural dynamics (ZND) models for solving this problem require complicated element-wise nonlinear activation functions and integral operations to obtain robust finite-time convergence, yielding a concern of error chattering and high computational cost. Different from previous ZND models, this paper proposes a novel ZND model called finite-time convergent neural dynamics (FTCND) model to synchronize diverse chaotic systems. With the adoption of norm operation, the proposed FTCND model realizes practical convergence in finite time without using conventional complex activation functions or integrators, showing strong robustness under bounded disturbances. Strict theoretical analysis for the FTCND model is given. The numerical experiments clearly demonstrate the performance and advantage of the FTCND model in comparison to another synchronization model, further verifying the effectiveness and superiority of the proposed FTCND model.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"151 ","pages":"Article 109122"},"PeriodicalIF":3.4,"publicationDate":"2025-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144623423","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}

{"title":"Stability of nonlinear time-varying systems with delayed stochastic impulses","authors":"Wenhao Song ,&nbsp;Luyao You ,&nbsp;Xiaodi Li","doi":"10.1016/j.cnsns.2025.109120","DOIUrl":"10.1016/j.cnsns.2025.109120","url":null,"abstract":"<div><div>This paper studies the exponential stability of nonlinear time-varying systems involving delayed impulses with stochastic intensity. Different from the deterministic delayed impulses, which are either stabilizing or destabilizing, stochastic impulsive intensity allows for the presence of both stabilizing and destabilizing impulses. When the system involves both stabilizing and destabilizing impulses, several Lyapunov-based conditions for exponential stability are presented. Due to the stochastic impulsive intensity and time delays, stabilizing impulses are allowed to transform into destabilizing impulses at some impulse instants. Specially, even when the system involves completely destabilizing impulses, the exponential stability can be achieved by providing a constrained attraction region. Two illustrated examples are presented to verify the effectiveness of the obtained results.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"151 ","pages":"Article 109120"},"PeriodicalIF":3.4,"publicationDate":"2025-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144621950","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}

{"title":"Fractional order entropy-based decision-making models under risk","authors":"Poulami Paul,&nbsp;Chanchal Kundu","doi":"10.1016/j.cnsns.2025.109106","DOIUrl":"10.1016/j.cnsns.2025.109106","url":null,"abstract":"<div><div>The construction of an efficient portfolio with a good level of return and minimal risk depends on selecting the optimal combination of stocks. This paper introduces a novel decision-making framework for stock selection based on fractional-order entropy due to Ubriaco. By tuning the fractional parameter <span><math><mi>α</mi></math></span>, the model captures varying attitudes of individuals toward risk. Values of <span><math><mi>α</mi></math></span> near 1 indicate high risk tolerance (adventurous attitude), while those near 0 reflect risk aversion (conservative attitude). The sensitivity of the fractional order entropy to changing risk preferences of decision-makers is demonstrated through four real-world portfolio models, namely, large-cap, mid-cap, diversified, and hypothetical. Furthermore, two new risk measures, termed as expected utility–fractional entropy (EU-FE) and expected utility–fractional entropy and variance (EU-FEV), are introduced to develop decision models aligned with investors’ risk preferences. The performance of the developed models are compared with existing decision-making approaches, thereby demonstrating its superiority and consistency. The effectiveness of the decision model is further tested with financial stock market data of PSI 20 index by finding efficient frontiers of portfolio with the aid of artificial neural network.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"152 ","pages":"Article 109106"},"PeriodicalIF":3.4,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144621951","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}

{"title":"The dynamic behavior of an eco-epidemiological prey-taxis model with infectious disease in prey","authors":"Zhangshuo Yan ,&nbsp;Wenjie Zhang ,&nbsp;Chunlai Mu ,&nbsp;Qiao Xin","doi":"10.1016/j.cnsns.2025.109105","DOIUrl":"10.1016/j.cnsns.2025.109105","url":null,"abstract":"<div><div>This study investigates an eco-epidemiological predator–prey model incorporating prey-taxis mechanism and infectious disease. Under the precondition that pathogens only spread within the prey species, the global existence and uniform boundedness of classical solutions are established in two dimensions. The results indicate that the prey-taxis mechanism does not result in population overcrowding. Subsequently, the large time behavior of its nonnegative constant steady states is obtained, revealing that disease invasion significantly impacts the dynamics of the resident predator–prey system. Notably, predator migration, especially with stronger predation, contributes to disease eradication. These findings offer valuable insights for disease control within prey populations, and can be applied to pest control through the release of predators and pathogens. To depict the impact of prey-taxis mechanism on its dynamic behaviors, we show that suitably large prey-taxis coefficients can destabilize the system at the coexistence steady state, triggering steady-state bifurcation and Hopf bifurcation. Numerical simulations are presented to validate these theoretical results, highlighting the complex interplay between disease dynamics, predator–prey interactions, and spatial movement.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"151 ","pages":"Article 109105"},"PeriodicalIF":3.4,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144606110","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}

{"title":"Identifying influential nodes in social networks considering heterogeneous cost","authors":"Wen Hu ,&nbsp;Ye Deng ,&nbsp;Yu Xiao ,&nbsp;Jun Wu","doi":"10.1016/j.cnsns.2025.109110","DOIUrl":"10.1016/j.cnsns.2025.109110","url":null,"abstract":"<div><div>With the rapid growth of online social platforms, the influence spread analysis in social networks has become increasingly important. Identifying influential nodes while considering both Influence Maximization (IM) and Influence Blocking Maximization (IBM) is a crucial issue in this field. In reality, the costs incurred by each user to participate as a seed in the diffusion process can vary significantly, prompting a focus on identifying influential nodes with heterogeneous cost. To address this, we introduce a two-player zero-sum static attack–defense game model considering cost heterogeneity. The attacker aims to maximize influence propagation while the defender aims to minimize it. By leveraging the equilibrium strategy of this game, we redefine the concept of influential nodes from the perspectives of attackers, defenders, and neutral observers. Experiments on scale-free networks and real-world networks demonstrate the significant impact of cost heterogeneity and resource constraints on the equilibrium strategy for both players. Specifically, when both players have equal available resources, the attacker always drops the critical nodes. As cost heterogeneity increases, the defender shifts from prioritizing critical nodes to abandoning them. This study advances the understanding of influential nodes with heterogeneous costs from an attack–defense game perspective and opens up new avenues for future research.</div></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":"151 ","pages":"Article 109110"},"PeriodicalIF":3.4,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144596774","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}