Physica D: Nonlinear Phenomena最新文献

{"title":"Effects of asymmetric rates and impulse interference in Rock-Paper-Scissors games","authors":"","doi":"10.1016/j.physd.2024.134384","DOIUrl":"10.1016/j.physd.2024.134384","url":null,"abstract":"<div><div>The dynamics of systems composed of cyclically competing species are complicated by the fact that they are strongly influenced by fluctuations. For this reason, it is attractive to study low-dimensional cycles where these impacts are most prominent. In this paper, we investigate the impacts of asymmetric compared to symmetric reactive rates on three-species biological diversity and spatial pattern formation in a four-state case using an RPS game model on a one-dimensional lattice. In addition, we also discuss the effects of interference thresholds on biodiversity maintenance when species are impulsively disturbed under both symmetric and asymmetric rates. The results show that enhancement of the competition rate promotes biodiversity while the mobility rate has the opposite effect when these rates being symmetric. Meanwhile, changes in reproductive rates have no direct effect on biodiversity. If rates are asymmetric, only one species survives and biodiversity is negatively affected. Conversely, the outcome of single species survival is altered when species are impulsively disturbed. Under symmetric rates, an increase in interference threshold results in a shift from coexistence of three species to survival of two species. With asymmetric rates, population dynamics change from the survival of only one species to the survival of two species if the interference is introduced. Our findings may enlighten people by RPS game model to protect endangered animals, or kill off harmful species, or to engineer cyclical population to stabilize the functionality of gene circuits for cancer treatment, or to guide election campaign.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322429","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Whitham modulation theory and Riemann problem for the Kundu–Eckhaus equation","authors":"","doi":"10.1016/j.physd.2024.134380","DOIUrl":"10.1016/j.physd.2024.134380","url":null,"abstract":"<div><div>In this paper, the Riemann problem for the defocusing Kundu–Eckhaus equation is investigated by Whitham modulation theory. First, we study the dispersion relation for linear waves. Then, the zero-phase and one-phase periodic solutions of the Kundu–Eckhaus equation along with the corresponding Whitham modulation equations are derived by the finite-gap integration method. Further, employing the Whitham equations parametrized by the Riemann invariants, the main fundamental wave structures induced by the discontinuous initial data are found. Analytical and graphic methods are utilized to provide the wave structures of rarefaction waves and dispersive shock waves, and thus for a complete classification of solutions under general step-like conditions of initial discontinuity.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142328187","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mathematical modeling of emission and control of carbon dioxide from infrastructure expansion activities","authors":"","doi":"10.1016/j.physd.2024.134387","DOIUrl":"10.1016/j.physd.2024.134387","url":null,"abstract":"<div><div>The rise in atmospheric carbon dioxide (<span><math><msub><mrow><mtext>CO</mtext></mrow><mrow><mn>2</mn></mrow></msub></math></span>) concentration has led to a rise in the global average surface temperatures. Deforestation and infrastructure expansion are key contributors to the increase in <span><math><msub><mrow><mtext>CO</mtext></mrow><mrow><mn>2</mn></mrow></msub></math></span> level. This study presents a non-linear mathematical model to explore the impact of infrastructure expansion on deforestation and rise in the atmospheric <span><math><msub><mrow><mtext>CO</mtext></mrow><mrow><mn>2</mn></mrow></msub></math></span> concentration. The proposed model considers the growth of infrastructure activities, driven by the increasing population, which in turn reduces the carrying capacity of forest biomass. The model is qualitatively analyzed to examine the system’s behavior in long run. It is found that a high growth rate of infrastructure expansion results in lower equilibrium level of forest biomass and higher <span><math><msub><mrow><mtext>CO</mtext></mrow><mrow><mn>2</mn></mrow></msub></math></span> concentrations. Moreover, for high population growth driven by infrastructure expansion, exceeding a critical level of infrastructure growth rate can cause the system to lose stability and generation of limit cycle oscillations through a supercritical Hopf-bifurcation. An increase in the growth rate coefficient of human population due to infrastructure expansion activities and deforestation rate can also lead to stability loss of interior equilibrium and existence of limit cycle oscillations in the system via Hopf-bifurcation. It is noticed that for critically high deforestation rate, the system may enter into transcritical bifurcation, resulting in the extinction of forest biomass. The study is extended to derive the strategies to effectively leverage existing mitigation options to reduce <span><math><msub><mrow><mtext>CO</mtext></mrow><mrow><mn>2</mn></mrow></msub></math></span> emissions from infrastructure expansion by taking efficiencies of mitigation options to cut the carbon dioxide emission rate and reduce the declination rate of carrying capacity of forest biomass resulting from infrastructure expansion as time-dependent control variables.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142322618","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Fluid flow between two parallel active plates","authors":"","doi":"10.1016/j.physd.2024.134373","DOIUrl":"10.1016/j.physd.2024.134373","url":null,"abstract":"<div><div>This paper investigates the fluid flow phenomenon arising from the combined action of two parallel plates, which can expand/squeeze, absorb/inject, and stretch/shrink at different rates. These physical mechanisms are incorporated into the governing unsteady Navier–Stokes equations, which are then reduced to a fourth-order nonlinear differential equation with boundary conditions reflecting the imposed wall constraints. By letting the permeable Reynolds number (controlling the nonlinear convective terms) limit to zero, we demonstrate the existence of exact solutions expressed in terms of advanced mathematical functions. Additionally, in the absence of wall expansion/contraction, elementary exponential solutions are obtained under particular relationships between the stretching/shrinking and permeability parameters. A shear-like exact solution with broader applicability across various physical parameters is also identified. For moderate values of the expansion/squeezing parameters and permeable Reynolds numbers, we propose an efficient double-expansion perturbation analysis to approximate the flow behavior. Otherwise, for general physical parameters, a comprehensive mathematical analysis is provided and numerical simulations are employed to extract insights into the complex fluid motion between the parallel plates.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142319530","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sundman theorem revisited","authors":"","doi":"10.1016/j.physd.2024.134385","DOIUrl":"10.1016/j.physd.2024.134385","url":null,"abstract":"<div><div>In this paper, we revisit Sundman’s Theorem on the three-body problem. We provide a simple example demonstrating that the requirement on the total angular momentum <span><math><mi>L</mi></math></span> (bounded away from zero) can be relaxed for a particular set of initial conditions, allowing double shocks. We present an explicit solution for the exact triple-collision scenario through a Sundman-like formal regularization.</div></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142318722","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Spatiotemporal analysis of a modified Leslie–Gower model with cross-diffusion and harvesting","authors":"","doi":"10.1016/j.physd.2024.134381","DOIUrl":"10.1016/j.physd.2024.134381","url":null,"abstract":"<div><p>This paper considers a modified Leslie–Gower prey–predator reaction–diffusion model introducing harvesting of both species. Both the temporal and spatiotemporal dynamics of the model have been examined. We have found the stability regions and drawn bifurcation diagrams to determine the harvesting effect on the model, revealing that the harvesting has a stabilizing effect. Local bifurcations, such as transcritical and Hopf bifurcations, appear in the temporal system. For the spatiotemporal model, Turing instability conditions have been determined. The amplitude equation for the critical modes has been derived using multiple time scale analyses by taking the harvesting effort as the bifurcating parameter. Also, we have verified the theoretical results by plotting several kinds of stationary patterns, including stripes, spots, and a mix of stripes and spots. This study’s critical observation is that as harvesting effort rises, the patterns steadily turn into spots, i.e., harvesting influences pattern creation strongly. This fosters a dynamic equilibrium, allowing competitors to maintain distance, optimize resource use and survive.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142274356","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Global attractor and its 1D and 2D structures of Beverton–Holt Ricker competition model","authors":"","doi":"10.1016/j.physd.2024.134354","DOIUrl":"10.1016/j.physd.2024.134354","url":null,"abstract":"<div><p>Beverton–Holt Ricker competition model is a planar difference system that describes intraspecific competition among individuals and interspecific competition. Known works investigated the stability of equilibria in some cases, showed the existence of stable 2-periodic points when there are no interior equilibria, and found numerically an attractor with riddled basin of attraction for some appropriate parameters. In this paper, we prove the existence of the global attractor, and give a complete description on qualitative properties and bifurcations of all equilibria except for some cases of high degeneracy. Moreover, we obtain different kinds of 1-dimensional or 2-dimensional structures of the global attractor, which were not considered in the known work.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142274354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multistability of state-dependent switched neural networks with Mexican-hat-type activation functions","authors":"","doi":"10.1016/j.physd.2024.134363","DOIUrl":"10.1016/j.physd.2024.134363","url":null,"abstract":"<div><p>This paper investigates the issue of multistability in state-dependent switched neural networks (SSNNs) with Mexican-hat-type activation functions (AFs). It establishes the coexistence and stability of multiple equilibrium points (EPs). Initially, the state space is partitioned based on the geometric characteristics of the Mexican-hat-type AF, enabling to determine the positions of the EPs. Secondly, the coexistence of <span><math><mrow><msup><mrow><mn>9</mn></mrow><mrow><msub><mrow><mi>h</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msup><msup><mrow><mn>7</mn></mrow><mrow><msub><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msup><msup><mrow><mn>5</mn></mrow><mrow><msub><mrow><mi>h</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></msup><msup><mrow><mn>3</mn></mrow><mrow><msub><mrow><mi>h</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></msup></mrow></math></span> EPs for <span><math><mi>n</mi></math></span>-neurons SSNNs under specific sufficient conditions is proved with the Brouwer’s fixed-point theorem. Next, by using diagonally dominant matrix theory and Gershgorin circle theorem, it is proven that there are <span><math><mrow><msup><mrow><mn>5</mn></mrow><mrow><msub><mrow><mi>h</mi></mrow><mrow><mn>1</mn></mrow></msub></mrow></msup><msup><mrow><mn>4</mn></mrow><mrow><msub><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></msup><msup><mrow><mn>3</mn></mrow><mrow><msub><mrow><mi>h</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></msup><msup><mrow><mn>2</mn></mrow><mrow><msub><mrow><mi>h</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></msup></mrow></math></span> asymptotically stable EPs under some conditions, where <span><math><mrow><msub><mrow><mi>h</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>,</mo><msub><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo><msub><mrow><mi>h</mi></mrow><mrow><mn>3</mn></mrow></msub></mrow></math></span> and <span><math><msub><mrow><mi>h</mi></mrow><mrow><mn>4</mn></mrow></msub></math></span> are nonnegative integers satisfying <span><math><mrow><mn>0</mn><mo>≤</mo><msub><mrow><mi>h</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>+</mo><msub><mrow><mi>h</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>+</mo><msub><mrow><mi>h</mi></mrow><mrow><mn>3</mn></mrow></msub><mo>+</mo><msub><mrow><mi>h</mi></mrow><mrow><mn>4</mn></mrow></msub><mo>≤</mo><mi>n</mi></mrow></math></span>. Therefore, we can obtain that SSNNs can have larger storage capacity by selecting the appropriate parameters <span><math><mrow><msub><mrow><mi>h</mi></mrow><mrow><mi>i</mi></mrow></msub><mo>,</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn></mrow></math></span>. Finally, the correctness of the results in this paper is verified through two numerical examples.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142240907","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Influences of artificial numerical noise on statistics and qualitative properties of chaotic system","authors":"","doi":"10.1016/j.physd.2024.134355","DOIUrl":"10.1016/j.physd.2024.134355","url":null,"abstract":"<div><p>Taking the nonlinear Schrödinger equation (NLSE) as an example, we provide from a mathematical viewpoint, rigorous evidence that numerical noise of a chaotic system as tiny artificial stochastic disturbances can increase exponentially to a macro-level. As a result, numerical simulations given by traditional algorithms in double precision may rapidly become badly polluted leading to huge deviations from the ‘true’ solution not only in trajectory but also, sometimes, even in statistics and/or some qualitative properties. Small physical disturbances in time and space are unavoidable in practice, which are often much larger than artificial numerical noise. So, from a physical viewpoint, it is wrong to neglect small spatio-temporal disturbances of a chaotic system: chaos should not be described by deterministic equations.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142274355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Learning on predictions: Fusing training and autoregressive inference for long-term spatiotemporal forecasts","authors":"","doi":"10.1016/j.physd.2024.134371","DOIUrl":"10.1016/j.physd.2024.134371","url":null,"abstract":"<div><p>Predictions of complex systems ranging from natural language processing to weather forecasting have benefited from advances in Recurrent Neural Networks (RNNs). RNNs are typically trained using techniques like Backpropagation Through Time (BPTT) to minimize one-step-ahead prediction loss. During testing, RNNs often operate in an auto-regressive mode, with the output of the network fed back into its input. However, this process can eventually result in exposure bias since the network has been trained to process ”ground-truth” data rather than its own predictions. This inconsistency causes errors that compound over time, indicating that the distribution of data used for evaluating losses differs from the actual operating conditions encountered by the model during training. Inspired by the solution to this challenge in language processing networks we propose the Scheduled Autoregressive Truncated Backpropagation Through Time (BPTT-SA) algorithm for predicting complex dynamical systems using RNNs. We find that BPTT-SA effectively reduces iterative error propagation in Convolutional and Convolutional Autoencoder RNNs and demonstrates its capabilities in the long-term prediction of high-dimensional fluid flows.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S016727892400321X/pdfft?md5=c5231aef9d912b65fa750a286252a7f5&pid=1-s2.0-S016727892400321X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142260724","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}