dorsal/arxiv
View Schema$C_{E}PT$ Symmetry of the Simple Ecological Dynamical Equations
| Authors | Vladan Pankovic, Rade Glavatovic, Milan Predojevic |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0510020 |
| URL | https://arxiv.org/abs/q-bio/0510020 |
Abstract
It is shown that all simple ecological, i.e. population dynamical equations (unlimited exponential population growth (or decrease) dynamics, logistic or Verhulst equation, usual and generalized Lotka-Volterra equations) hold a symmetry, called $C_{E}PT$ symmetry. Namely, all simple ecological dynamical equations are invariant (symmetric) in respect to successive application of the time reversal transformation - $T$, space coordinates reversal or parity transformation - $P$, and predator-prey reversal transformation - $C_{E}$ that changes preys in the predators or pure (healthy) in the impure (fatal) environment, and vice versa. It is deeply conceptually analogous to remarkable $CPT$ symmetry of the fundamental physical dynamical equations. Further, it is shown that by more accurate, "microscopic" analysis, given $C_{E}PT$ symmetry becomes explicitly broken.
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"abstract": "It is shown that all simple ecological, i.e. population dynamical equations\n(unlimited exponential population growth (or decrease) dynamics, logistic or\nVerhulst equation, usual and generalized Lotka-Volterra equations) hold a\nsymmetry, called $C_{E}PT$ symmetry. Namely, all simple ecological dynamical\nequations are invariant (symmetric) in respect to successive application of the\ntime reversal transformation - $T$, space coordinates reversal or parity\ntransformation - $P$, and predator-prey reversal transformation - $C_{E}$ that\nchanges preys in the predators or pure (healthy) in the impure (fatal)\nenvironment, and vice versa. It is deeply conceptually analogous to remarkable\n$CPT$ symmetry of the fundamental physical dynamical equations. Further, it is\nshown that by more accurate, \"microscopic\" analysis, given $C_{E}PT$ symmetry\nbecomes explicitly broken.",
"arxiv_id": "q-bio/0510020",
"authors": [
"Vladan Pankovic",
"Rade Glavatovic",
"Milan Predojevic"
],
"categories": [
"q-bio.PE"
],
"title": "$C_{E}PT$ Symmetry of the Simple Ecological Dynamical Equations",
"url": "https://arxiv.org/abs/q-bio/0510020"
},
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