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We introduce a delay nonlinear differential equation model which describes how fish are harvested. In our previous studies we investigated the persistence of that equation and existence of a periodic solution for this equation. Here we…
Life systems are complex and hierarchical, with diverse components at different scales, yet they sustain themselves, grow, and evolve over time. How can a theory of such complex biological states be developed? Here we note that for a…
This work concerns the dynamics of a certain class of delay differential equations (DDEs) which we refer to as state dependent delay maps. These maps are generated by delay differential equations where the derivative of the current state…
Evolutionary complexity is here measured by the number of trials/evaluations needed for evolving a logical gate in a non-linear medium. Behavioural complexity of the gates evolved is characterised in terms of cellular automata behaviour. We…
In this paper we study well-posedness and asymptotic stability for a class of nonlinear second-order evolution equations with intermittent delay damping. More precisely, a delay feedback and an undelayed one act alternately in time. We show…
Prompted by the recent more precise determination of the basic cosmological parameters and growing evidence that the matter-energy content of the universe is now dominated by dark energy and dark matter we present the general solution of…
We deal with a class of second order in time nonlinear evolution equations with state-dependent delay. This class covers several important PDE models arising in the theory ofnonlinear plates. Our first result states well-posedness in a…
Retarded stochastic differential equations (SDEs) constitute a large collection of systems arising in various real-life applications. Most of the existing results make crucial use of dissipative conditions. Dealing with "pure delay" systems…
Long-term memory is a feature observed in systems ranging from neural networks to epidemiological models. The memory in such systems is usually modeled by the time delay. Furthermore, the nonlocal operators, such as the "fractional order…
Density perturbations and their dynamic evolution from early to late times can be used for an improved understanding of interesting physical phenomena both in cosmology and in the context of heavy-ion collisions. We discuss the spectrum and…
The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces…
An alternative approach - nonequilibrium evolution thermodynamics, is compared with classical Landau approach. A statistical justification of the approach is carried out with help of probability distribution function on an example of a…
The problem of error growth due to the incomplete knowledge of the evolution law which rules the dynamics of a given physical system is addressed. Major interest is devoted to the analysis of error amplification in systems with many…
In this article we consider a class of state-dependent delay differential equations which is modelling the dynamics of the number of adult trees in forests. We prove the boundedness of solutions for a single species model as well as a…
Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…
We present simulations of a hard disc system and analyze the time evolution of the dynamic heterogeneities. We characterize the time evolution of slow regions and slow particles individually. The motion of slow clusters turns out to be very…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
In the past years, a remarkable mapping has been found between the dynamics of a population of M individuals undergoing random mutations and selection, and that of a single system in contact with a thermal bath with temperature 1/M. This…
In this chapter we review concepts and theories of polymer dynamics. We think of it as an introduction to the topic for scientists specializing in other subfields of statistical mechanics and condensed matter theory, so, for the readers…
We study evolutes and involutes of space curves. Although much of the material presented is not new and can be found in classic treatises, we believe that a modern and unified treatment, complemented with several novel observations, may be…