The Lynx and Hare Data of 200 Years as the Nonlinear Conserving Interaction Based on Noether’s Conservation Laws and Stability

Uechi, Hiroshi; Uechi, Lisa; Uechi, Schun T.

doi:10.4236/jamp.2021.911181

Cited by 3 publications

(1 citation statement)

References 48 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The bifurcation phenomena and solutions in nonlinear differential equations were first reported and discussed by Henri Poincaré in 1885 [1], and the bifurcation theory and classification of solutions have been studied as the property of the nonlinear differential equation with constant coefficients (NDE-CC). The nonlinear dynamical systems have been studied in the vast fields of physical, chemical, molecular and biological systems [2] [3] [4] [5]. Though several independent solutions to nonlinear differential equations are often found, it is not possible to combine the known solutions to construct new solutions.…”

Section: The Bifurcation Solutions and Bifurcation-integration Soluti...mentioning

confidence: 99%

Thermomechanical Dynamics (TMD) and Bifurcation-Integration Solutions in Nonlinear Differential Equations with Time-Dependent Coefficients

Uechi,

Uechi

2024

JAMP

Self Cite

View full text Add to dashboard Cite

The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple backand-forth motion develops into water drinking motion. The solution to a drinking bird equation of motion manifests itself the transition from thermodynamic equilibrium to nonequilibrium irreversible states. The independent solution signifying a nonequilibrium thermal state seems to be constructed as if two independent bifurcation solutions are synthesized, and so, the solution is tentatively termed as the bifurcation-integration solution. The bifurcation-integration solution expresses the transition from mechanical and thermodynamic equilibrium to a nonequilibrium irreversible state, which is explicitly shown by the nonlinear differential equation with time-dependent coefficients (NDE-TC). The analysis established a new theoretical approach to nonequilibrium irreversible states, thermomechanical dynamics (TMD).The TMD method enables one to obtain thermodynamically consistent and time-dependent progresses of thermodynamic quantities, by employing the bifurcation-integration solutions of NDE-TC. We hope that the basic properties of bifurcation-integration solutions will be studied and investigated further in mathematics, physics, chemistry and nonlinear sciences in general.

show abstract

Section: The Bifurcation Solutions and Bifurcation-integration Soluti...mentioning

confidence: 99%

Thermomechanical Dynamics (TMD) and Bifurcation-Integration Solutions in Nonlinear Differential Equations with Time-Dependent Coefficients

Uechi,

Uechi

2024

JAMP

Self Cite

View full text Add to dashboard Cite

show abstract

Thermoelectric Stirling Engine (TEG-Stirling Engine) Based on the Analysis of Thermomechanical Dynamics (TMD)

Uechi,

Uechi

2024

JAMP

View full text Add to dashboard Cite

The Method of Thermoelectric Energy Generations Based on the Axial and Radial Flux Electromagnetic Inductions<sup>*</sup>

Uechi,

Uechi

2024

WJET

View full text Add to dashboard Cite

The Lynx and Hare Data of 200 Years as the Nonlinear Conserving Interaction Based on Noether’s Conservation Laws and Stability

Cited by 3 publications

References 48 publications

Thermomechanical Dynamics (TMD) and Bifurcation-Integration Solutions in Nonlinear Differential Equations with Time-Dependent Coefficients

Thermomechanical Dynamics (TMD) and Bifurcation-Integration Solutions in Nonlinear Differential Equations with Time-Dependent Coefficients

Thermoelectric Stirling Engine (TEG-Stirling Engine) Based on the Analysis of Thermomechanical Dynamics (TMD)

The Method of Thermoelectric Energy Generations Based on the Axial and Radial Flux Electromagnetic Inductions<sup>*</sup>

Contact Info

Product

Resources

About