The effects of a distributed 'weak generic kernel' delay on cyclically coupled limit cycle and chaotic oscillators are considered. For coupled Van der Pol oscillators (and in fact, other oscillators as well) the delay can produce transitions from amplitude death(AD) or oscillation death (OD) to Hopf bifurcation-induced periodic behavior, with the delayed limit cycle shrinking or growing as the delay is varied towards or away from the bifurcation point respectively. The transition from AD to OD is mediated here via a pitchfork bifurcation, as seen earlier for other couplings as well. Also, the cyclically coupled undelayed van der Pol system here is already in a state of AD/OD, and introducing the delay allows both oscillations and AD/OD as the delay parameter is varied. This is in contrast to other limit cycle systems, where diffusive coupling alone does not result in the onset of AD/OD. For systems where the individual oscillators are chaotic, such as a Sprott oscillator system or a coupled van der Pol-Rayleigh system with parametric forcing, the delay may produce AD/OD (as in the Sprott case), with the AD to OD transition now occurring via a transcritical bifurcation instead. However, this may not be possible, and the delay might just vary the attractor shape. In either of these situations however, increased delay strength tends to cause the system to have simpler behavior, streamlining the shape of the attractor, or shrinking it in cases with oscillations.

In this paper, spatial patterns of a diffusive Tumor cell and immune cell model with sigmoid ratio-dependent functional response are investigated. The asymptotic stability behavior of the corresponding nonspatial model around the unique positive interior equilibrium point in homogeneous steady state is obtained. We have obtained the optimal condition under which the system loses stability and a Turing pattern occurs. Numerical simulations have been carried out in order to show the significant role of reaction-diffusion coefficients and other important parameters of the system. Various contour figures of spatial patterns through Turing instability are portrayed and analyzed in order to substantiate the applicability of the present model. The paper ends with an extended discussion of biological implications of the immune system.

Prey refuge and additional food provided to predator help in balancing the population in ecology. In this paper, we have analysed a fractional Holling Type-II predator-prey model with prey refuge and additional food to predator. Existence and uniqueness of solution is established with the help of existing theory of fractional calculus. Sufficient conditions for existence and stability of equilibrium points are derived. Effect of prey refuge and quality of additional food to predator on balancing the population is crucially analyzed. Theoretical results are supported by numerical simulations.

This work investigates the entropy generation in nanofluid flow in a sloping channel with Navier slip and asymmetric wall temperatures. The viscosity and thermal conductivity are assumed to be dependent on temperature. The equations governing the flow, temperature are nonlinear and are solved using Homotopy Analysis Method (HAM) after non-dimensionalisation. Comparisons with existing literature have been produced and are found to be in excellent agreement, for special case of the current formulation. The impact of pertinent flow and fluid parameters on entropy generation, Bejan number, Nusselt number and skin friction is addressed, developed and displayed graphically.

The problem of feed-forward control of overhead crane system is discussed. By combining the Kalman's controllability theory and Hartman-Grobman theorem from dynamical system theory, a linear, continuous state feedback-based feed-forward controller that stabilizes the crane system at the desired end position of payload is designed. The efficacy of proposed controller is demonstrated by comparing the simulation experiment results for overhead crane with/without time-varying length of hoisting rope.

The human~respiratory~and~cardiovascular~systems get affected from surrounding atmosphere. Systematic study of indoor and outdoor pollution is needed for better understanding of their global epidemiology. In this substantial body of research, a mathematical model for transmission of asthma in a variable size population under the effects of indoor smoke and outdoor air pollution is proposed. In addition, the reproduction number for the dynamical system is formulated which signifies the intensity of asthma exacerbation. The global and local stability of acquired equilibrium points is studied. The performance of the model is simulated numerically which illustrates how polluted environment effectively increases levels of aeroallergens and their effect on asthma exacerbation, and how such exposures can be meaningfully reduced.

This article describes a mathematical model for a predator-prey system with two types of functional responses and a transmissible disease in the predator species. The effect of stocking of healthy predator in healthy predator species class and harvesting of healthy predator are analyzed. The essential mathematical features of the proposed eco-epidemic system such as boundedness, positivity, local and global stability and Hopf bifurcation are discussed. Numerical simulations are also performed to validate the theoretical results obtained.