Abstract
A conservation law along with stability, recovering phenomena, and characteristic patterns of a nonlinear dynamical system have been studied and applied to physical, biological, and ecological systems. In our previous study, we proposed a system of symmetric 2n-dimensional conserved nonlinear differential equations. In this paper, competitive systems described by a 2-dimensional nonlinear dynamical (ND) model with external perturbations are applied to population cycles and recovering phenomena of systems from microbes to mammals. The famous 10-year cycle of population density of Canadian lynx and snowshoe hare is numerically analyzed.We find that a nonlinear dynamical system with a conservation law is stable and generates a characteristic rhythm (cycle) of population density,whichwe call the standard rhythm of a nonlinear dynamical system. The stability and restoration phenomena are strongly related to a conservation law and the balance of a system. The standard rhythm of population density is a manifestation of the survival of the fittest to the balance of a nonlinear dynamical system.
| Original language | English |
|---|---|
| Article number | 103J01 |
| Journal | Progress of Theoretical and Experimental Physics |
| Volume | 2013 |
| Issue number | 10 |
| DOIs | |
| Publication status | Published - 2013 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Physics and Astronomy(all)
Cite this
Stability and restoration phenomena in competitive Systems. / Uechi, Lisa; Akutsu, Tatsuya.
In: Progress of Theoretical and Experimental Physics, Vol. 2013, No. 10, 103J01, 2013.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Stability and restoration phenomena in competitive Systems
AU - Uechi, Lisa
AU - Akutsu, Tatsuya
PY - 2013
Y1 - 2013
N2 - A conservation law along with stability, recovering phenomena, and characteristic patterns of a nonlinear dynamical system have been studied and applied to physical, biological, and ecological systems. In our previous study, we proposed a system of symmetric 2n-dimensional conserved nonlinear differential equations. In this paper, competitive systems described by a 2-dimensional nonlinear dynamical (ND) model with external perturbations are applied to population cycles and recovering phenomena of systems from microbes to mammals. The famous 10-year cycle of population density of Canadian lynx and snowshoe hare is numerically analyzed.We find that a nonlinear dynamical system with a conservation law is stable and generates a characteristic rhythm (cycle) of population density,whichwe call the standard rhythm of a nonlinear dynamical system. The stability and restoration phenomena are strongly related to a conservation law and the balance of a system. The standard rhythm of population density is a manifestation of the survival of the fittest to the balance of a nonlinear dynamical system.
AB - A conservation law along with stability, recovering phenomena, and characteristic patterns of a nonlinear dynamical system have been studied and applied to physical, biological, and ecological systems. In our previous study, we proposed a system of symmetric 2n-dimensional conserved nonlinear differential equations. In this paper, competitive systems described by a 2-dimensional nonlinear dynamical (ND) model with external perturbations are applied to population cycles and recovering phenomena of systems from microbes to mammals. The famous 10-year cycle of population density of Canadian lynx and snowshoe hare is numerically analyzed.We find that a nonlinear dynamical system with a conservation law is stable and generates a characteristic rhythm (cycle) of population density,whichwe call the standard rhythm of a nonlinear dynamical system. The stability and restoration phenomena are strongly related to a conservation law and the balance of a system. The standard rhythm of population density is a manifestation of the survival of the fittest to the balance of a nonlinear dynamical system.
UR - http://www.scopus.com/inward/record.url?scp=84888629545&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84888629545&partnerID=8YFLogxK
U2 - 10.1093/ptep/ptt077
DO - 10.1093/ptep/ptt077
M3 - Article
VL - 2013
JO - Progress of Theoretical and Experimental Physics
JF - Progress of Theoretical and Experimental Physics
SN - 2050-3911
IS - 10
M1 - 103J01
ER -