In this paper, we consider a stochastic Gilpin-Ayala population model with Markovian switching and white noise. All parameters are influenced by stochastic perturbations. We analyze the existence of global positive solution, asymptotic stability in probability, pth moment exponential stability, extinction, weak persistence, stochastic permanence and stationary distribution of the model, which g...

We present a sufficient condition for robust permanence of ecological (or Kolmogorov) differential equations based on average Liapunov functions. Via the minimax theorem we rederive Schreiber’s sufficient condition [S. Schreiber, J. Differential Equations, 162 (2000), pp. 400–426] in terms of Liapunov exponents and give various generalizations. Then we study robustness of permanence criteria ag...

Verifiable criteria are established for the permanence and existence of positive periodic solutions of a delayed discrete predator-prey model with monotonic functional response. It is shown that the conditions that ensure the permanence of this system are similar to those of its corresponding continuous system. And the investigations generalize some well-known results. In particular, a more acc...

The growing dropout and low permanence of rural students in higher education has become a central problem the system, both affecting quality conditions training programmes preventing materialisation benefits that achieving this educational level entails for society. However, study these events populations is scarce, resulting an inadequate treatment and, consequently, impossibility consolidatin...

here, a predator-prey model with hassell-varley type functional responses is studied. some sufficient conditions are obtained for the permanence and global asymptotic stability of the system by using comparison theorem and constructing a suitable lyapunov functional. moreover, an example is illustrated to verify the results by simulation.

Abstract In this paper, we discuss biological background and mathematical analysis of glioma gene therapy for contributing to cancer treatment. By a reactiondiffusion system, we model interactions between gliom cells and viruses. We establish some sufficient conditions on model parameters which guarantee the permanence of the system and the existence of periodic solutions. Our study has experim...

OBJECTIVE To show the complications that increase the permanence at intensive care unit (ICU) of the patients submitted to cardiac surgery. METHODS Eighty-five handbooks of patients submitted to cardiac surgery had been analyzed, retrospectively, from March to May 2009 at Santa Casa de Misericórdia de Juiz de Fora (MG)--Brazil--and 14 (16.47%) patients had been studied. They remained more tha...

The permanence of a single-species population discrete model with feedback control is considered. We found that if we use the method of comparison theorem, then the additional condition, to some extent, is necessary. But for the system itself, this condition may not be necessary. Here, we use new methods instead of the comparison theorem to get the permanence of the system in consideration; the...