International Journal of Biomathematics

Astrocytes have potential to break synchrony between neurons. Authors' recent researches reveal that astrocytes vary the synchronization threshold and provide an appropriate feedback control in stabilizing neural activities. In this study, we propose an astrocyte-inspired controller for desynchronization of two coupled limit-cycle oscillators as a minimal network model. The design procedure consists of two parts. First, based on the astrocyte model, the structure of the dynamic controller is suggested. Then, to have an efficient controller, parameters of controller are tuned through an optimization algorithm. The proposed bio-inspired controller takes advantages of three important properties: (1) the controller desynchronizes the oscillators without any undesirable effects (e.g. stopping, annihilating or starting divergent oscillations); (2) it consumes little effort to preserve the desirable desynchronized state; and (3) the controller is robust with respect to parameters' variations. Simulation results reveal the ability of the proposed controller.

A competitive system on the n-rectangle: {x ∈ Rⁿ: 0 ≤ x_i ≤ l_i, i = 1, …, n} was considered, each species of which, in isolation, admits logistic growth with the hyperbolic structure saturation. It has an (n - 1)-dimensional invariant surface called carrying simplex Σ as a globe attractor, hence the long term dynamics of the system is completely determined by the dynamics on Σ. For the three-dimensional system, the whole dynamical behavior was presented. It has a unique positive equilibrium point and any limit set is either an equilibrium point or a limit cycle. The system is permanent and it is proved that the number of periodic orbits is finite and non-periodic oscillation the May–Leonard phenomenon does not exist. A criterion for the positive equilibrium to be globally asymptotically stable is provided. Whether there exist limit cycles or not remains open.

In this paper, we have studied a general kind of n-species Lotka–Volterra network-like food-chain system with delays and impulses on time scales. Applying Mawhin's continuation theorem of coincidence degree theory and some skills of inequalities, some sufficient criteria have been established to guarantee the existence of at least 2ⁿ periodic solutions to this model. One example is given to illustrate the effectiveness of our results.

In the current critique, we deliberate the blood flow through narrowing vein with a stenosis in the manifestation of heat and mass transmission. The non-Newtonian flora of blood in small veins are examined mathematically by demonstrating the blood as Carreau fluid. The illustration for the blood flow is debated through an axially irregular but outward regular stenosis. Regularity in the dissemination of the fortification clipping stress and resistive impedance and their evolution with the emerging stenosis is a new significant feature of our investigation. Analytical solutions have been appraised for "velocity, temperature, concentration, resistance impedance, wall shear stress and shearing stress at the stenosis throat". The graphical consequences of different types of tapering arteries (i.e. "converging tapering, diverging tapering, non-tapered artery") have been studied for dissimilar constraints of attention. Rivulet shapes have been strategized for different parameters at the culmination of the article.

The aim of this paper is to present a continuum model for bioconvection of oxytactic micro-organisms in a non-Darcy porous medium and to investigate the effects of bioconvection and mixed convection on the steady boundary layer flow past a horizontal plate embedded in a porous medium filled with a water-based nanofluid. The governing partial differential equations for momentum, heat, oxygen and micro-organism conservation are reduced to a set of nonlinear ordinary differential equations using similarity transformations that are numerically solved using a built-in MATLAB ODE solver. The effects of the bioconvection parameters on the nanofluid fluid properties, nanoparticle concentration and the density of the micro-organism are analyzed. A comparative analysis of our results with those previously reported in the literature is given. Among the significant findings in this study is that bioconvection parameters highly influence heat, mass and motile micro-organism transfer rates.

Hepatitis C virus (HCV) is a blood-borne infection that can lead to progressive liver failure, cirrhosis, hepatocellular carcinoma and death. A deterministic mathematical model for assessing the impact of daily intravenous drug misuse on the transmission dynamics of HCV is presented and analyzed. A threshold quantity known as the reproductive number has been computed. Stability of the steady states has been investigated. The dynamical analysis reveals that the model has globally asymptotically stable steady states. The impact of daily intravenous drug misuse on the transmission dynamics of HCV has been discussed through the basic reproductive number and numerical simulations.

A delayed predator–prey diffusion system with homogeneous Neumann boundary condition is considered. In order to study the impact of the time delay on the stability of the model, the delay τ is taken as the bifurcation parameter, the results show that when the time delay across some critical values, the Hopf bifurcations may occur. In particular, by using the normal form theory and the center manifold reduction for partial functional differential equations, the direction of the Hopf bifurcation and the stability of the bifurcated periodic solution have been established. The effect of the diffusion on the bifurcated periodic solution is also considered. A numerical example is given to support the main result.

In this paper, a nonlinear mathematical model is proposed and analyzed to study the role of dissolved oxygen (DO)-dependent bacteria on biodegradation of one or two organic pollutant(s) in a water body. In the case of two organic pollutant(s), it is assumed that the one is fast degrading and the other is slow degrading and both are discharged into the water body from outside with constant rates. The density of bacteria is assumed to follow logistic model and its growth increases due to biodegradation of one or two organic pollutant(s) as well as with the increase in the concentration of DO. The model is analyzed using the stability theory of differential equations and by simulation. The model analysis shows that the concentration(s) of one or both organic pollutant(s) decrease(s) as the density of bacteria increases. It is noted that for very large density of bacteria, the organic pollutant(s) may be removed almost completely from the water body. It is found that simulation analysis confirms the analytical results. The results obtained in this paper are in line with the experimental observations published in literature.

Synchronization behavior of an ensemble of unidirectionally coupled neurons with a constant input is investigated. Chemical synapses are considered for coupling. Each neuron is also considered to be exposed to a self-delayed feedback. The synchronization phenomenon is analyzed by the error dynamics of the response trajectories of the system. The effect of various model parameters e.g. coupling strength, feedback gain and time delay, on synchronization is also investigated and a measure of synchrony is computed in each cases. It is shown that the synchronization is not only achieved by increasing the coupling strength, the system also required to have a suitable feedback gain and time delay for synchrony. Robustness of the parameters for synchrony is verified for larger systems.

This paper constructs a mathematical model for blood flow through an artery with mild stenosis. Constitutive equations for Carreau fluid are employed in the mathematical modeling. Analysis has been carried out in the presence of constant magnetic field. Symmetric and asymmetric shapes of stenosis are taken. Governing flow model is computed for the series solution. The flow quantities of interest, for instance, axial velocity, pressure gradient, pressure drop, impedance and shear stress at the walls of stenotic artery are described for various pertinent parameters entering into the problem.