Dynamics of a magnetic gear with two cogging-free operation modes

The coupling of two rotating spherical magnets is investigated experimentally. For two specific angles between the input and output rotation axes, a cogging-free coupling is observed, where the driven magnet is phase-locked to the driving one. The striking difference between these two modes of operation is the reversed sense of rotation of the driven magnet. For other angles, the experiments reveal a more complex dynamical behavior, which is divided in three different classes. This is done by analyzing the deviation from a periodic motion of the driven magnet, and by measuring the total harmonic distortion of this rotation. The experimental results can be understood by a mathematical model based on pure dipole–dipole interaction, with the addition of adequate friction terms.

Density-Dependent Population Growth

The observation that no population can grow indefinitely and that most populations persist on ecological timescales implies that mechanisms of population regulation exist. Feedback mechanisms include competition for limited resources, cannibalism, and predation rates that vary with density. Density dependence occurs when per capita birth or death rates depend on population density. Density dependence is compensatory when the population growth rate decreases with population density and depensatory when it increases. The logistic model incorporates density dependence as a simple linear function. A population exhibiting logistic growth will reach a stable population size. Non-linear density-dependent terms can give rise to multiple equilibria. With discrete time models or time delays in density-dependent regulation, the approach to equilibrium may not be smooth—complex dynamical behavior is possible. Density-dependent feedback processes can compensate, up to a point, for natural and anthropogenic disturbances; beyond this point a population will collapse.

Adaptive Synchronization of Fractional-Order Coupled Neurons Under Electromagnetic Radiation

In this paper, we investigate the dynamical characteristics of four-variable fractional-order Hindmarsh–Rose neuronal model under electromagnetic radiation. The numerical results show that the improved model exhibits more complex dynamical behavior with more bifurcation parameters. Meanwhile, based on the fractional-order Lyapunov stability theory, we propose two adaptive control methods with a single controller to realize chaotic synchronization between two coupled neurons. Finally, numerical simulations show the feasibility and effectiveness of the presented method.

Efficient optimal families of higher-order iterative methods with local convergence

The main aim of this manuscript is to propose two new schemes having three and four substeps of order eight and sixteen, respectively. Both families are optimal in the sense to Kung-Traub conjecture. The derivation of them are based on the weight function approach. In addition, theoretical and computational properties are fully investigated along with two main theorems describing the order of convergence. Further, we also provide the local convergence of them in Banach space setting under weak conditions. From the numerical experiments, we find that they perform better than the existing ones when we checked the performance of them on a concrete variety of non- linear scalar equations. Finally, we analyze the complex dynamical behavior of them which also provide a great extent to this.