Related papers: Punctuated evolution due to delayed carrying capac…
In complex systems, the interplay between nonlinear and stochastic dynamics, e.g., J. Monod's necessity and chance, gives rise to an evolutionary process in Darwinian sense, in terms of discrete jumps among attractors, with punctuated…
We consider a logistic differential equation subject to impulsive delayed harvesting, where the deduction information is a function of the population size at the time of one of the previous impulses. A close connection to the dynamics of…
The main topic of this thesis is the analysis of evolution equations reflecting issues in ecology and population dynamics. In mathematical modelling, the impact of environmental elements and the interaction between species is read into the…
We introduce a simple computational model that, with a microscopic dynamics driven by natural selection and mutation alone, allows the description of true speciation events. A statistical analysis of the so generated evolutionary tree…
A nonlinear inequality is formulated in the paper. An estimate of the rate of decay of solutions to this inequality is obtained. This inequality is of interest in a study of dynamical systems and nonlinear evolution equations. It can be…
In this paper, we show that different types of evolutionary game dynamics are, in principle, special cases of a dynamical system model based on our previously reported framework of generalized growth transforms. The framework shows that…
In this paper we consider second order evolution equations with unbounded dynamic feedbacks. Under a regularity assumption we show that observability properties for the undamped problem imply decay estimates for the damped problem. We…
In this paper, we consider a linear heat equation with constant coefficients and a single constant delay. Such equations are commonly used to model and study various problems arising in ecology and population biology when describing the…
In this work we study a kinetic model of active particles with delayed dynamics, and its limit when the number of particles goes to infinity. This limit turns out to be related to delayed differential equations with random initial…
A general nonlinear logistic equation has been proposed to model long-time saturation in industrial growth. An integral solution of this equation has been derived for any arbitrary degree of nonlinearity. A time scale for the onset of…
The well-defined but intricate course of time evolution exhibited by many naturally occurring phenomena suggests some source of dynamic order sustaining it. In spite of its obviousness as a problem, it has remained absent from the…
Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We here present a generic stochastic model…
It is generally recognized that a distinguishing feature of life is its peculiar capability to avoid equilibration. The origin of this capability and its evolution along the timeline of abiogenesis is not yet understood. We propose to study…
If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as…
The long-term behaviour of dynamic systems can be classified in two different regimes, regular or chaotic, depending on the values of the control parameters, which are kept constant during the time evolution. Starting from slightly…
A general system of difference equations is presented for multispecies communities with density dependent population growth and delayed maturity. Interspecific competition, mutualism, predation, commensalism, and amensalism are…
We study general stochastic birth and death processes including delay. We develop several approaches for the analytical treatment of these non-Markovian systems, valid, not only for constant delays, but also for stochastic delays with…
This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
Non-ideal deterministic system "tank with liquid-electric motor" is studied. Two delay-approximation models are considered. Impact of the delay on the emergence, evolution and disappearance of regular and chaotic limit sets (attractors) of…