Non-equilibrium thermodynamics of ecosystems: Entropic analysis of stability and diversity

Lyapunov stability of competitive cells dynamics in tumor mechanobiology

“…Inequality (17) then actually states a substantial equivalence between the thermodynamical and stability of the multi-species dynamics, in the light of the fact that the entropy principle can be attributed to the study of the stability of the Lyapunov function of the generalized VL system at hand, a key parallel for the present application that has been also deeply investigated (without considering mechanical coupling) in the field of ecological models in Ref. [71]. By virtue of the Lyapunov stability theorem assessments, one can suppose that, in the neighbourhood of an equilibrium point φ * , the dissipation potential can assume the following expression:…”

Le Chatelier's principle in replicator dynamics

“…By analogy to phenomenological non-equilibrium thermodynamics, (34) is sometimes presented as the statement of the Le Chatelier principle for population dynamics; see [45] and references therein. We stress that (34) is only a necessary condition for the local principle.…”

RETRACTED: Stability analysis of community and ecosystem hierarchies using the Lyapunov method

“…Some researchers have discussed alternative strategies for studying ecosystem stability, such as stochastic methods, Lyapunov stability theory, steady state, non-equilibrium thermodynamics, etc. (Chakrabarti and Ghosh, 2009;Li, 1995;Michaelian, 2005;Svetlosanov, 1985). The most complex systems are generally considered to be landscapes consisting of nested ecological systems.…”