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A new delay equation is introduced to describe the punctuated evolution of complex non-linear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a population in the four main regimes dominated respectively by: (i) gain and competition, (ii) gain and cooperation, (iii)… (More)

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 Lotka-Volterra… (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: sym-biosis 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 "… (More)

- Vyacheslav I. Yukalov, Elizaveta 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)

The method of self-similar factor approximants is shown to be very convenient for solving different evolution equations and boundary-value problems typical of physical applications. The method is general and simple, being a straightforward two-step procedure. First, the solution to an equation is represented as an asymptotic series in powers of a variable.… (More)

- V I Yukalov, E P Yukalova
- 2008

The method of self-similar factor approximants is applied to calculating the critical exponents of the O(N)-symmetric ϕ 4 theory and of the Ising glass. It is demonstrated that this method, being much simpler than other known techniques of series summa-tion in calculating the critical exponents, at the same time, yields the results that are in very good… (More)

- V I Yukalov, E P Yukalova
- 1997

The state of art in studying thermodynamic properties of hot and dense nuclear matter is reviewed with the special emphasis on the confinement–deconfinement transition between hadron matter and quark–gluon plasma. The most popular models used for describing deconfinement are analysed, including statistical bootstrap models, pure phase models, the model of… (More)

- V I Yukalov, E P Yukalova
- 2000

Collective phenomena in strongly nonequilibrium systems interacting with electromagnetic field are considered. Such systems are described by complicated non-linear 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)

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)