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A class of models is introduced describing the evolution of population species whose carrying capacities are functionals of these populations. The functional dependence of the carrying capacities reflects the fact that the correlations between populations can be realized not merely through direct interactions, as in the usual predator-prey LotkaVolterra… (More)

We introduce a general mathematical model of symbiosis between different entities by taking into account the influence of each species on the carrying capacities of the others. The modeled entities can pertain to biological and ecological societies or to social, economic and financial societies. Our model includes three basic types: symbiosis with direct… (More)

- Vyacheslav I. Yukalov, E. P. Yukalova, Didier Sornette
- I. J. Bifurcation and Chaos
- 2014

We consider a class of evolution equations describing population dynamics in the presence of a carrying capacity depending on the population with delay. In an earlier work, we presented an exhaustive classification of the logistic equation where the carrying capacity is linearly dependent on the population with a time delay, which we refer to as the “linear… (More)

- Vyacheslav I. Yukalov, E. P. Yukalova, Didier Sornette
- PloS one
- 2013

We present a novel system of equations to describe the evolution of self-organized structured societies (biological or human) composed of several trait groups. The suggested approach is based on the combination of ideas employed in the theory of biological populations, system theory, and utility theory. The evolution equations are defined as utility rate… (More)

Many illnesses are associated with an alteration of the immune system homeostasis due to a combination of factors, including exogenous bacterial insult, endogenous breakdown (e.g., development of a disease that results in immuno suppression), or an exogenous hit like surgery that simultaneously alters immune responsiveness and provides access to bacteria,… (More)

A method is suggested for treating those complicated physical problems for which exact solutions are not known but a few approximation terms of a calculational algorithm can be derived. The method permits one to answer the following rather delicate questions: What can be said about the convergence of the calculational procedure when only a few its terms are… (More)

Collective phenomena in strongly nonequilibrium systems interacting with electromagnetic field are considered. Such systems are described by complicated nonlinear differential or integro–differential equations. The aim of this review is to show that many nonlinear collective phenomena can be successfully treated by a recently developed method called the… (More)

A novel model of biological organisms is advanced, treating an organism as a self-consistent system subject to a pathogen flux. The principal novelty of the model is that it describes not some parts, but a biological organism as a whole. The organism is modeled by a five-dimensional dynamical system. The organism homeostasis is described by the evolution… (More)

Coherent resonance is the effect of resonant excitation of nonlinear coherent modes in trapped Bose condensates. This novel effect is shown to be feasible for Bosecondensed trapped gases. Conditions for realizing this effect are derived. A method of stabilizing Bose condensates with attractive interactions is advanced. The origin of dynamic critical… (More)

An overview is given of different approaches to describing the process of deconfinement in quantum chromodynamics. The analysis of the known approaches demonstrates that the detailed picture of how deconfinement really occurs has not yet been understood. Therefore, one has to be rather cautious when interpreting experimental signals as attributed to… (More)