Positive periodic solutions for an impulsive ratio-dependent predator-prey system with delays.
Positive periodic solutions for nonlinear difference equations via a continuation theorem.
Positive periodic solutions of functional differential equations and population models.
Positive periodic solutions of functional discrete systems and population models.
Positive periodic solutions of neutral logistic difference equations with multiple delays.
Positive solutions of a neutral difference equation with positive and negative coefficients.
Positive solutions of a renewal equation
An existence theorem is proved for the scalar convolution type integral equation .
Positive solutions of nonlinear delay integral equations modelling epidemics and population growth.
Possibly Longest Food Chain: Analysis of a Mathematical Model
We consider the number of trophic levels in a food chain given by the equilibrium state for a simple mathematical model with ordinary differential equations which govern the temporal variation of the energy reserve in each trophic level. When a new trophic level invades over the top of the chain, the chain could lengthen by one trophic level. We can derive the condition that such lengthening could occur, and prove that the possibly longest chain is globally stable. In some specific cases,...
Practical persistence for differential delay models of population interactions.
Pravděpodobnost vymření kontinuální kultivace
Precise spectral asymptotics for nonautonomous logistic equations of population dynamics in a ball.
Propagation of Growth Uncertainty in a Physiologically Structured Population
In this review paper we consider physiologically structured population models that have been widely studied and employed in the literature to model the dynamics of a wide variety of populations. However in a number of cases these have been found inadequate to describe some phenomena arising in certain real-world applications such as dispersion in the structure variables due to growth uncertainty/variability. Prompted by this, we described two recent...
Qualitative behavior of giving up smoking models.
Qualitative properties of a predator-prey model with delay.
Random coefficient differential models of growth of anaerobic photosynthetic bacteria.
Random coefficients bifurcating autoregressive processes
This paper presents a new model of asymmetric bifurcating autoregressive process with random coefficients. We couple this model with a Galton−Watson tree to take into account possibly missing observations. We propose least-squares estimators for the various parameters of the model and prove their consistency, with a convergence rate, and asymptotic normality. We use both the bifurcating Markov chain and martingale approaches and derive new results in both these frameworks.
Rational Constants of Generic LV Derivations and of Monomial Derivations
We describe the fields of rational constants of generic four-variable Lotka-Volterra derivations. Thus, we determine all rational first integrals of the corresponding systems of differential equations. Such systems play a role in population biology, laser physics and plasma physics. They are also an important part of derivation theory, since they are factorizable derivations. Moreover, we determine the fields of rational constants of a class of monomial derivations.
Reaction-diffusion systems: stabilizing effect of conditions described by quasivariational inequalities
Reaction-diffusion systems are studied under the assumptions guaranteeing diffusion driven instability and arising of spatial patterns. A stabilizing influence of unilateral conditions given by quasivariational inequalities to this effect is described.
Reclassification, diversity and elementary number theory