Sustainable theory of a logistic model - Fisher information approach

Avan Al-Saffar, Eun jin Kim

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)


Information theory provides a useful tool to understand the evolution of complex nonlinear systems and their sustainability. In particular, Fisher information has been evoked as a useful measure of sustainability and the variability of dynamical systems including self-organising systems. By utilising Fisher information, we investigate the sustainability of the logistic model for different perturbations in the positive and/or negative feedback. Specifically, we consider different oscillatory modulations in the parameters for positive and negative feedback and investigate their effect on the evolution of the system and Probability Density Functions (PDFs). Depending on the relative time scale of the perturbation to the response time of the system (the linear growth rate), we demonstrate the maintenance of the initial condition for a long time, manifested by a broad bimodal PDF. We present the analysis of Fisher information in different cases and elucidate its implications for the sustainability of population dynamics. We also show that a purely oscillatory growth rate can lead to a finite amplitude solution while self-organisation of these systems can break down with an exponentially growing solution due to the periodic fluctuations in negative feedback.

Original languageEnglish
Pages (from-to)81-91
Number of pages11
JournalMathematical Biosciences
Early online date2 Jan 2017
Publication statusPublished - Mar 2017
Externally publishedYes


  • Driving parameters
  • Fisher information
  • Nonlinear system
  • Probability density function(PDF)
  • Sustainability

ASJC Scopus subject areas

  • Statistics and Probability
  • Medicine(all)
  • Modelling and Simulation
  • Immunology and Microbiology(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics


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