International Journal of Biomathematics

The unique Hamiltonian description of neuro- and psycho-dynamics at the macroscopic, classical, inter-neuronal level of brain's neural networks, and microscopic, quantum, intra-neuronal level of brain's microtubules, is presented in the form of an open Liouville equation. This implies the arrow of time in both neuro- and psycho-dynamic processes and proves the existence of the formal neuro-biological space-time self-similarity. This proof implies the existence of a unique neurodynamical law, which acts on different scales of brain's functioning.

A discrete time periodic n-species Lotka–Volterra type competitive model with delays is investigated. By using Gaines and Mawhin's continuation theorem based on the coincidence degree theory, a new sufficient condition on the existence of positive periodic solutions of the model is established.

In this paper, we establish a new sufficient condition of the permanence for the Lotka–Volterra cooperative systems with multiple discrete delays by extending the results in [Nakata and Muroya, Permanence for nonautonomous Lotka–Volterra cooperative systems with delays, Nonlinear Anal. RWA., in press]. Our condition holds even if the instantaneous feedback does not dominate over the total of the interspecific interactions and does not need the restriction on the size of time delays, different from the results in [Lu and Lu, Permanence for two-species Lotka–Volterra cooperative systems with delays, Math. Biosci. Eng.5 (2008) 477–484]. We offer an example for comparison with the previous results and numerical results supporting our theoretical analysis are given.

In this paper, a class of interval projection neural networks for solving quadratic programming problems are investigated. By using Gronwall inequality and constructing appropriate Lyapunov functionals, several novel conditions are derived to guarantee the exponential stability of the equilibrium point. Compared with previous results, the conclusions obtained here are suitable not only to convex quadratic programming problems but also to degenerate quadratic programming problems, and the conditions are more weaker than the earlier results reported in the literature. In addition, one numerical example is discussed to illustrate the validity of the main results.

In this paper, we study the interaction of peristalsis with heat transfer for the flow of a viscous fluid through a porous medium in uniform and nonuniform channels. The flow is subjected to constant transverse magnetic field. Long wavelength approximation (that is, the wavelength of the peristaltic wave is large compared with the radius of the channel) is used to solve the governing system. Closed form expressions are derived for the pressure–flow relationship, temperature, and heat transfer coefficient. The effects of various physical parameters are discussed through graphs.

First, we obtain a new result for the permanence of a well known delayed discrete-time model of single species. Second, based on this new condition, we discuss the permanence of a delayed discrete-time predator–prey model in which the prey disperses in two patches with biased dispersion. The biological implications of the results are briefly discussed.

Introducing discrete time delay into the model for producing 1, 3-propanediol by microbial continuous fermentation, the stability and Hopf bifurcation of a delay differential system for microorganisms in continuous culture are considered in this paper, including the changing regularity of bifurcation value and oscillating period. Algebraic criteria for absolute stability, as well as the transversality condition for Hopf bifurcation of this kind system are obtained. Explicit algorithm for determining the direction of Hopf bifurcation and the stability of periodic solution is derived, using the theory of normal form and center manifold. Finally, numerical simulations show the effectiveness of our results. The pictures of periodic solutions and phase planes with specified parameters suggest that our results can qualitatively describe oscillatory phenomena occurring in experiments.

In this paper, the cumulative effect of ecological factors in the habitat on the spread of tuberculosis (TB) in human population is modeled and analyzed. The total human population is divided into two classes, susceptibles and infectives. It is assumed that TB is not only spread by direct contacts with infectives in the population but also indirectly by bacteria which are emitted by infectives in the habitat. It is assumed further that bacteria survive due to conducive ecological factors such as flower pots, plants, grasses, human clothes, etc. in the habitat. The cumulative density of ecological factors in the habitat is assumed to be governed by a population density dependent logistic model. The analysis of the model shows that as parameters governing the conducive ecological factors in the habitat increase, the spread of TB increases. The same result is also found with the increase in the parameter governing the survival and accumulation of bacteria in the habitat. It is further found that due to immigration of the population TB becomes more endemic. A numerical study of the model is also carried out to support the analytical results.

A tuberculosis (TB) model with two latent periods, short-term latent period (E₁) and long-term latent period (E₂), and fast and slow progressions is analyzed. The stability of the unique endemic equilibrium of the model is proved. It turns out that the disease-free equilibrium is globally asymptotically stable if the basic reproduction number R₀ ≤ 1, and the endemic equilibrium is globally asymptotically stable if R₀ > 1.

In this paper, we introduce and study an impulsive mutualistic model with variable coefficients. By using Floquent theorem, the invasion threshold and the stability of the boundary periodic solution are obtained. Furthermore, by using standard techniques of bifurcation theory, the existent condition of the positive periodic solution is obtained. Finally, numerical simulations are carried out to confirm the main theorems.

This paper is devoted to global exponential stability of reaction-diffusion time-varying delayed cellular neural networks with Dirichlet boundary conditions. Without assuming the monotonicity and differentiability of activation functions, nor symmetry of synaptic interconnection weights, the authors present some delay independent and easily verifiable sufficient conditions to ensure the global exponential stability of the equilibrium solution by using the method of variational parameter and inequality technique. These conditions obtained have important leading significance in the designs and applications of global exponential stability for reaction-diffusion neural circuit systems with delays. Lastly, one example is given to illustrate the theoretical analysis.

A semi-stochastic model is developed and investigated for human immunodeficiency virus type-1 (HIV-1) population dynamics. The model includes both stochastic parts (changes of CD4+ T cells) and deterministic parts (changes of free virions). Using the best currently available parameter values, we estimate the distributions of the time of occurrence and the magnitude of the early peak in virions. We investigated the effects of varying parameter values on mean solutions in order to assess the stochastic effects of between-patient variability. Numerical simulation shows that the lower the infection rate, the higher the death rate of the infected cells, more rapid clearance of virions and lower rate of virion emission by the infected cells result in lower speed of infection progression and magnitude but a greater variability in response. We also examine the probability that a small viral inoculum fails to establish an infection. Further, we theoretically quantify the expected variability around the infected equilibrium for each population by using diffusion approximation.