We applied <em>n</em>-variable conserving nonlinear differential equations (<em>n</em>-CNDEs) to the population data of the 10-year cycles of Canadian lynx (1821-2016) and the snowshoe hare (18...We applied <em>n</em>-variable conserving nonlinear differential equations (<em>n</em>-CNDEs) to the population data of the 10-year cycles of Canadian lynx (1821-2016) and the snowshoe hare (1845-1921). Modeling external effects as perturbations to population dynamics, recovering and restorations from disintegrations (or extinctions), stability and survival strategies are discussed in terms of the conservation law inherent to dynamical interactions among species. The 2-variable conserving nonlinear interaction (2CNIs) is extended to 3, 4, ... <em>n</em>-variable conserving nonlinear interactions (<em>n</em>-CNIs) of species by adjusting minimum unknown parameters. The population cycle of species is a manifestation of conservation laws existing in complicated ecosystems, which is suggested from the CNDE analysis as <em>a standard rhythm</em> of interactions. The ecosystem is a consequence of the long history of nonlinear interactions and evolutions among life-beings and the natural environment, and the population dynamics of an ecosystem are observed as approximate CNIs. Physical analyses of the conserving quantity in nonlinear interactions would help us understand why and how they have developed. The standard rhythm found in nonlinear interactions should be considered as a manifestation of the survival strategy and the survival of the fittest to the balance of biological systems. The CNDEs and nonlinear differential equations with time-dependent coefficients would help find useful physical information on the survival of the fittest and symbiosis in an ecosystem.展开更多
Conceptually,radii are amongst the simplest Poincaré-invariant properties that can be associated with hadrons and light nuclei.Accurate values of these quantities are necessary so that one may judge the character...Conceptually,radii are amongst the simplest Poincaré-invariant properties that can be associated with hadrons and light nuclei.Accurate values of these quantities are necessary so that one may judge the character of putative solutions to the strong interaction problem within the Standard Model.However,limiting their ability to serve in this role,recent measurements and new analyses of older data have revealed uncertainties and imprecisions in the radii of the proton,pion,kaon,and deuteron.In the context of radius measurement using electron+hadron elastic scattering,the past decade has shown that reliable extraction requires minimisation of bias associated with practitioner-dependent choices of data fitting functions.Different answers to that challenge have been offered;and this perspective describes the statistical Schlessinger point method(SPM),in unifying applications to proton,pion,kaon,and deuteron radii.Grounded in analytic function theory,independent of assumptions about underlying dynamics,free from practitioner-induced bias,and applicable in the same form to diverse systems and observables,the SPM returns an objective expression of the information contained in any data under consideration.Its robust nature and versatility make it suitable for use in many branches of experiment and theory.展开更多
文摘We applied <em>n</em>-variable conserving nonlinear differential equations (<em>n</em>-CNDEs) to the population data of the 10-year cycles of Canadian lynx (1821-2016) and the snowshoe hare (1845-1921). Modeling external effects as perturbations to population dynamics, recovering and restorations from disintegrations (or extinctions), stability and survival strategies are discussed in terms of the conservation law inherent to dynamical interactions among species. The 2-variable conserving nonlinear interaction (2CNIs) is extended to 3, 4, ... <em>n</em>-variable conserving nonlinear interactions (<em>n</em>-CNIs) of species by adjusting minimum unknown parameters. The population cycle of species is a manifestation of conservation laws existing in complicated ecosystems, which is suggested from the CNDE analysis as <em>a standard rhythm</em> of interactions. The ecosystem is a consequence of the long history of nonlinear interactions and evolutions among life-beings and the natural environment, and the population dynamics of an ecosystem are observed as approximate CNIs. Physical analyses of the conserving quantity in nonlinear interactions would help us understand why and how they have developed. The standard rhythm found in nonlinear interactions should be considered as a manifestation of the survival strategy and the survival of the fittest to the balance of biological systems. The CNDEs and nonlinear differential equations with time-dependent coefficients would help find useful physical information on the survival of the fittest and symbiosis in an ecosystem.
基金Supported by the National Natural Science Foundation of China(12135007)Natural Science Foundation of Jiangsu Province(BK20220122)STRONG-2020"The strong interaction at the frontier of knowledge:fundamental research and applications"which received funding from the European Union's Horizon 2020 research and innovation programme(824093)。
文摘Conceptually,radii are amongst the simplest Poincaré-invariant properties that can be associated with hadrons and light nuclei.Accurate values of these quantities are necessary so that one may judge the character of putative solutions to the strong interaction problem within the Standard Model.However,limiting their ability to serve in this role,recent measurements and new analyses of older data have revealed uncertainties and imprecisions in the radii of the proton,pion,kaon,and deuteron.In the context of radius measurement using electron+hadron elastic scattering,the past decade has shown that reliable extraction requires minimisation of bias associated with practitioner-dependent choices of data fitting functions.Different answers to that challenge have been offered;and this perspective describes the statistical Schlessinger point method(SPM),in unifying applications to proton,pion,kaon,and deuteron radii.Grounded in analytic function theory,independent of assumptions about underlying dynamics,free from practitioner-induced bias,and applicable in the same form to diverse systems and observables,the SPM returns an objective expression of the information contained in any data under consideration.Its robust nature and versatility make it suitable for use in many branches of experiment and theory.
