Chaos, Solitons and Fractals: X最新文献

{"title":"On the fractal geometry of different heart rhythms","authors":"Tahmineh Azizi","doi":"10.1016/j.csfx.2022.100085","DOIUrl":"10.1016/j.csfx.2022.100085","url":null,"abstract":"<div><p>In this study, we explore the possibility that ECG recordings belong to class of multifractal process for which a large number of scaling exponents are required to characterize their scaling structures. We use the BIDMC Congestive Heart Failure database including long term ECG recordings from 11 men, aged 22 to 71, and 4 women, aged 54 to 63 with severe congestive heart failure and the MIT-BIH Arrhythmia database that contains 48 half-hour excerpts of two-channel ambulatory ECG recordings, obtained from 47 subjects studied by the BIH Arrhythmia Laboratory between 1975 and 1979. We compare these two chronic heart diseases with the control people in the MIT-BIH Normal Sinus Rhythm database which includes 18 long-term ECG recordings of 5 men, aged 26 to 45, and 13 women, aged 20 to 50 without significant arrhythmia. The vibration analysis such as power spectral densities (PSD) analysis has been performed for differentiating the time series. Multifractal dynamics of heartbeat interval signals have been assessed by multifractal spectrum analysis to differentiate normal signals with arrhythmia and severe congestive heart failure patients. We apply Higuchi algorithm to find the fractal complexity of each cardiac rhythm and then compare the signals for different time intervals. According to our analysis, we investigate that neither the power spectral densities nor the Higuchi algorithm to find the fractal dimension alone were sufficient to separate different classes of patients and healthy people. However, when multifractal analysis and scaling exponent were used as a classifier, the three classes were well separated. In addition, multifractal analysis revealed that we have a narrow range of exponents for arrhythmia and congestive heart failure subjects and as a result, a clear loss of multifractality for them. It was of great significance to show that we have a narrower range of exponents for arrhythmia subject compared to congestive heart failure subject which is useful to recognize these two classes of patients with heart disease. Our findings provide a comprehensive framework for diagnostic and classifying different patients with cardiac disease such as arrhythmia and congestive heart failure and differentiate them with normal people without heart disease which is crucial in finding the best diagnostic and controlling strategy in fight against chronic heart disease.</p></div>","PeriodicalId":37147,"journal":{"name":"Chaos, Solitons and Fractals: X","volume":"9 ","pages":"Article 100085"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590054422000148/pdfft?md5=10b1e6e4e7bf058f69a98f9d4efc3666&pid=1-s2.0-S2590054422000148-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88360353","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamics of bitcoin prices and energy consumption","authors":"Moinak Maiti","doi":"10.1016/j.csfx.2022.100086","DOIUrl":"10.1016/j.csfx.2022.100086","url":null,"abstract":"<div><p>The present study examines the nonlinear relationship between the bitcoin prices and total bitcoin energy consumption over the period November 2010 and October 2021. A discrete threshold regression (TR) model is deployed to estimate the unknown thresholds that trigger the Bitcoin prices regime change. The designated TR model identifies six regimes of change for Bitcoin price movements. The estimated critical threshold specifications (total bitcoin energy consumption) that trigger the regime change of Bitcoin prices are estimated as 0.13, 2.52, 14.06, 43.17, and 146.29 respectively. The study finds that the impact of total bitcoin energy consumption on bitcoin prices are only statistically significant in the higher (4^th and 6^th) regimes respectively. The message here is that the impact of total bitcoin energy consumption on bitcoin prices is not uniform.</p></div>","PeriodicalId":37147,"journal":{"name":"Chaos, Solitons and Fractals: X","volume":"9 ","pages":"Article 100086"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S259005442200015X/pdfft?md5=bb4d5e7d9288017dbf660b33048393d1&pid=1-s2.0-S259005442200015X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90361080","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Prime numbers and the evolution of cooperation, II: Advantages to cooperators using prime-number period lengths in a finite population constrained to prisoner's dilemma strategies that alternate between periods of activity and inactivity","authors":"Tim Johnson","doi":"10.1016/j.csfx.2022.100079","DOIUrl":"10.1016/j.csfx.2022.100079","url":null,"abstract":"<div><p>This paper presents a model of a finite population of agents constrained to strategies that alternate between activity and inactivity (a.k.a. temporal partitioning) in a social environment where multiple one-shot prisoner's dilemma games occur across discrete, intra-generational time points. Evolutionary selection acts on agents’ behavioral dispositions to cooperate/defect and the schedules that determine when agents periodically implement that behavior. Numerical simulation of the model indicates that cooperators reach fixation with far greater frequency when using schedules with prime-number period lengths. These findings reinforce recent analytic findings that indicate a connection between the evolution of cooperation and the prime numbers, plus they offer new empirical predictions about the timing of social behavior.</p></div>","PeriodicalId":37147,"journal":{"name":"Chaos, Solitons and Fractals: X","volume":"9 ","pages":"Article 100079"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590054422000094/pdfft?md5=3d85510476a7f3fa3ba4b416940530c2&pid=1-s2.0-S2590054422000094-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78158557","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Analysis of time-fractional non-linear Kawahara Equations with power law kernel","authors":"Irfan Ullah,&nbsp;Amir Ali,&nbsp;Sayed Saifullah","doi":"10.1016/j.csfx.2022.100084","DOIUrl":"10.1016/j.csfx.2022.100084","url":null,"abstract":"<div><p>In this article, we study time-fractional non-linear Kawahara and modified Kawahara equations with Caputos fractional derivative. A variety of integral transforms with Adomian decomposition are applied to obtain the general series solutions of the considered models. The efficiency of the proposed methods is confirmed by numerical examples under suitable initial conditions. From the numerical results, one can see that the attained series solutions converge to the exact solutions of the systems. The stability of the applied methods is investigated using the principle of Banach contraction and <span><math><mi>S</mi></math></span>-stable mapping. For the Kawahara Equation, it is observed that the amplitude of the system enhances as time increases for fixed values of fractional orders. Similarly, for stable temporal variables, when the fractional-order increases, the amplitude of the solitary wave solution also increases. Similarly, for the modified system, the wave amplitude is also enhanced with variations in time <span><math><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></math></span>. It infers that when <span><math><mrow><mo>(</mo><mi>α</mi><mo>)</mo></mrow></math></span> increases, it significantly decreases the wave amplitude. It is also observed that uniform changes take place in the wave amplitude with time <span><math><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow></math></span>. However, non-uniform changes in wave amplitude occur for different values of <span><math><mi>α</mi></math></span>. The absolute error between the exact and obtained series solutions is presented. It is revealed that the absolute error in the systems reduces promptly when <span><math><mi>x</mi></math></span> increases at a comparatively small time <span><math><mi>t</mi></math></span>, whereas the increment in iterations decreases the error in the systems.</p></div>","PeriodicalId":37147,"journal":{"name":"Chaos, Solitons and Fractals: X","volume":"9 ","pages":"Article 100084"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590054422000136/pdfft?md5=a17bb5eebeff4f1965528565e4a0a564&pid=1-s2.0-S2590054422000136-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73666775","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Prime numbers and the evolution of cooperation, I: A prisoner's dilemma model that identifies prime numbers via invasions of cooperators","authors":"Tim Johnson","doi":"10.1016/j.csfx.2022.100081","DOIUrl":"10.1016/j.csfx.2022.100081","url":null,"abstract":"<div><p>The development of methods to identify prime numbers spans centuries and includes models of physical and biological systems that spot primes. This paper adds to the latter research genre by reporting a prisoner's dilemma model that identifies prime numbers greater than 2. Albeit containing unconventional features and arguable assumptions, the model nonetheless confirms a previously hypothesized connection between prime numbers and the cross-disciplinary puzzle of how cooperation evolved. In a companion paper (part II), the features and assumptions of the analytic model reported here are explored in a finite-population, computational model.</p></div>","PeriodicalId":37147,"journal":{"name":"Chaos, Solitons and Fractals: X","volume":"9 ","pages":"Article 100081"},"PeriodicalIF":0.0,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590054422000112/pdfft?md5=706c8f217373a8e6d9e3682d49393538&pid=1-s2.0-S2590054422000112-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80735732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Mechanisms of stable species coexistence in food chain systems: Strength of odor disturbance and group defense","authors":"Wangjun Xu ,&nbsp;Daiyong Wu ,&nbsp;Jian Gao ,&nbsp;Chuansheng Shen","doi":"10.1016/j.csfx.2022.100073","DOIUrl":"https://doi.org/10.1016/j.csfx.2022.100073","url":null,"abstract":"<div><p>Odor disturbance and group defense generally play an important role in ecosystem stability. By incorporating odor disturbances and group defenses into the traditional three-species food chain system, where the preys are disturbed by the odor of predators, and group together to defend. We proved the boundedness of solutions of the system, and discussed the existence of equilibrium points. By Lyapunov’s first method and Routh-Hurwitz criterion, the sufficient conditions for stability of equilibrium points are obtained. It is found that, with the increasing of group defense, the density of the preys increases, while the odor disturbance of predators decreases the density of preys. Interestingly, the group defense induces a transition from a boundary equilibrium point to a positive equilibrium one, or from no Hopf-bifurcation to a Hopf-bifurcation. Furthermore, we demonstrated that the system undergoes a saddle-node bifurcation at <span><math><mrow><msub><mi>m</mi><mi>c</mi></msub><mo>=</mo><mn>0.3362</mn></mrow></math></span>, below which the system has a stable node and a saddle point, suggesting that the less odor disturbance avail system stability; while above which the system has no equilibrium point, indicating that the greater odor disturbance causes the collapse of the system. To reveal the underlying mechanisms of the interplay of odor disturbance and group defense, the bifurcation diagrams of the preys with two factors are given respectively.</p></div>","PeriodicalId":37147,"journal":{"name":"Chaos, Solitons and Fractals: X","volume":"8 ","pages":"Article 100073"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590054422000033/pdfft?md5=c03aac623bd29c0583b5c8f47cb29ef4&pid=1-s2.0-S2590054422000033-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"109128408","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Solitary wave solutions of GKP equation with (2+1)dimensional variable-coefficients in dynamic systems","authors":"Zhen ZHAO ,&nbsp;Jing PANG","doi":"10.1016/j.csfx.2021.100069","DOIUrl":"10.1016/j.csfx.2021.100069","url":null,"abstract":"<div><p>At present, the solution and qualitative analysis of nonlinear partial differential equations occupy a very important position in the study of dynamics. In this paper, the bilinear Bäcklund transformation of the (2+1)-dimensional variable-coefficient <span><math><mrow><mi>G</mi><mi>a</mi><mi>r</mi><mi>d</mi><mi>n</mi><mi>e</mi><mi>r</mi><mo>−</mo><mi>K</mi><mi>P</mi><mo>(</mo><mi>G</mi><mi>K</mi><mi>P</mi><mo>)</mo></mrow></math></span> equation is deduced by virtue of Hirota bilinear form, which consists of seven bilinear equations and involves ten arbitrary parameters. On the basis of the bilinear Bäcklund transformation, the traveling wave solution of the equation is obtained. Then the test function of the interaction solution of the positive quadratic function and exponential function of the (2+1)-dimensional variable-coefficient <span><math><mrow><mi>G</mi><mi>K</mi><mi>P</mi></mrow></math></span> equation is constructed, and then the test function of the positive quadratic function, hyperbolic cosine function and the interaction solution of the cosine function is constructed. With the help of mathematical symbol software Maple and Mathematica, the solitary wave solutions of (2+1)-dimensional variable-coefficient <span><math><mrow><mi>G</mi><mi>K</mi><mi>P</mi></mrow></math></span> equation is obtained by using Maple and Mathematica, and the interaction phenomena between a Lump wave and a Kink wave, a Lump wave and Multi-Kink waves are discussed.</p></div>","PeriodicalId":37147,"journal":{"name":"Chaos, Solitons and Fractals: X","volume":"8 ","pages":"Article 100069"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590054421000142/pdfft?md5=13c67829da3df92fe85d3f9ec17ee478&pid=1-s2.0-S2590054421000142-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41831913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A fractional mathematical modeling of protectant and curative fungicide application","authors":"Pushpendra Kumar ,&nbsp;Vedat Suat Erturk ,&nbsp;V. Govindaraj ,&nbsp;Sunil Kumar","doi":"10.1016/j.csfx.2022.100071","DOIUrl":"https://doi.org/10.1016/j.csfx.2022.100071","url":null,"abstract":"<div><p>Fungicides are consumed to foreclose or slow the epidemics of disease germ by fungi. Crop cultivation is a favorable business platform for farmers, but it is also very common for them to have losses. These losses happen by attacking pathogens, such as fungi, oomycetes (water fungi), viruses, bacteria, nematodes, and viroid that spread the infection into the plants. In this article, we derive a fractional mathematical model for simulating the dynamics of fungicide application via Caputo-Fabrizio fractional derivative. Caputo-Fabrizio operator is defined with non-singular type kernel which is better than singular kernel. We give some important proofs related to the existence of a unique solution of the given model. We derive the solution of the model by using the Adams-Bashforth algorithm and also mentioned the stability of the method. We plotted the number of graphs at different fungicide application rate, fungicide decay rate, fungicide effectiveness, curatives rate of fungicide, growth rate of the host, and removal rate. A complete structure of the given problem can be understood by this paper. The main novelty of this work is to understand the role of fungicide application in the disease caused by fungi with the help of fractional derivatives consisting memory effects.</p></div>","PeriodicalId":37147,"journal":{"name":"Chaos, Solitons and Fractals: X","volume":"8 ","pages":"Article 100071"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S259005442200001X/pdfft?md5=fa0f2ccf4eb27f9b80fdb6a20b3cafa0&pid=1-s2.0-S259005442200001X-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136895824","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The fractional view analysis of the Navier-Stokes equations within Caputo operator","authors":"Hassan Khan ,&nbsp;Qasim Khan ,&nbsp;Poom Kumam ,&nbsp;Hajira ,&nbsp;Fairouz Tchier ,&nbsp;Said Ahmed ,&nbsp;Gurpreet Singh ,&nbsp;Kanokwan Sitthithakerngkiet","doi":"10.1016/j.csfx.2022.100076","DOIUrl":"10.1016/j.csfx.2022.100076","url":null,"abstract":"<div><p>In this research article the residual power series method is implemented for the solution of the Navier-stokes equations with two and three dimensions having the initial conditions. Caputo operator is used for the fractional derivative. The formulation is made in general form and then applied to the specific problems to check the validity of the suggested method. The solution of some numerical examples of the Navier-stokes equations are presented for both fractional and integer orders of the problems. The comparison of the obtained and exact solution is provided by using 2D and 3D plots of the solutions which confirmed the higher accuracy of the proposed method. Tables are drawn to show the results obtained, exact solutions and absolute error of the suggested method for each problem. It is investigated that as the number of terms increase in the series solution of the problems, the obtained solutions have the closed contact with actual solutions of each problem. From the calculated values it is cleared that the method is accurate and easy and therefore can be extended further to linear and nonlinear problems.</p></div>","PeriodicalId":37147,"journal":{"name":"Chaos, Solitons and Fractals: X","volume":"8 ","pages":"Article 100076"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590054422000069/pdfft?md5=c1a46d9123af2c3432de6566709d2150&pid=1-s2.0-S2590054422000069-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74341060","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Dynamical analysis of the transmission of dengue fever via Caputo-Fabrizio fractional derivative","authors":"Salah Boulaaras ,&nbsp;Rashid Jan ,&nbsp;Amin Khan ,&nbsp;Muhammad Ahsan","doi":"10.1016/j.csfx.2022.100072","DOIUrl":"10.1016/j.csfx.2022.100072","url":null,"abstract":"<div><p>In this work, we develop a sophisticated mathematical model for dengue transmission dynamics based on vaccination, reinfection and carrier class assumptions. We utilize Caputo-Fabrizio fractional framework to represent the transmission phenomena of dengue. For the model analysis, the basic theory and findings of the Caputo-Fabrizio fractional operator are provided. We utilize the next-generation approach to calculate the threshold parameter <span><math><msub><mi>R</mi><mn>0</mn></msub></math></span> for our proposed dengue infection model. We have shown that the disease-free steady-state of the hypothesized dengue system is locally asymptotically stable if <span><math><mrow><msub><mi>R</mi><mn>0</mn></msub><mo>&lt;</mo><mn>1</mn></mrow></math></span> and is unstable in other conditions. The reproduction number of the system of dengue infection is investigated numerically. Furthermore, under the Caputo-Fabrizio approach, we offer a numerical approach for solving our fractional-order problem. We obtain the solution pathways of our system with various values of fractional-order <span><math><mi>ϑ</mi></math></span> and other input values in order to illustrate the effects of fractional-order <span><math><mi>ϑ</mi></math></span> and other input values on our system. Based on our findings, we forecast the most essential system factors for eradicating dengue infections.</p></div>","PeriodicalId":37147,"journal":{"name":"Chaos, Solitons and Fractals: X","volume":"8 ","pages":"Article 100072"},"PeriodicalIF":0.0,"publicationDate":"2022-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S2590054422000021/pdfft?md5=fdac609f7a514e3f22b62622d671e4d4&pid=1-s2.0-S2590054422000021-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46441868","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}