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This paper considers the problem: if coexistence occurs in the long run when a third species w invades an ecosystem consisting of two species u and v on , where u, v and w compete with one another. Under the assumption that the influence of w on u and v is small and other suitable conditions, we show that the three species can coexist as a non-monotone travelling wave. Such type of non-monotone waves plays an important role in the study of three-species phenomena. However, fewer results are known for the existence of such waves in the literature. Our approach, based on the method of sub- and super-solutions and bifurcation theory, provides a new approach to construct non-monotone waves of this type. Moreover, we show that the waves we construct are stable. To the best of our knowledge, this is the first rigorous result of stability for such type of waves.

A cascoded GaN half-bridge with a wide-band galvanically isolated current sensor is proposed. A 650 V depletion-mode GaN field-effect transistor is switched by a low-propagation-delay gate driver in active-mode. The standby and active modes are switched by a 25 V N-ch laterally diffused MOS (LDMOS). The current sensor uses the LDMOS as a shunt resistor, gm-cell-based sense amplifier and a mixer-based isolation amplifier for wider bandwidth. PVT variations of on-resistance of the current-detecting MOSFET are compensated using a reference MOSFET. A digital calibration loop across the isolation is formed to keep the current sensor gain constant within ± 1.5 % across the whole temperature range. The wide-band current sensor can measure the power device switching current. In this study, a cascoded GaN half-bridge switching and inductor current sensing using low-side and high-side device current are demonstrated. The proposed techniques show the possibility of implementing a GaN half-bridge module with an isolated current sensor in a package.

We deal with a two-component system of reaction–diffusion equations with conservation of mass in a bounded domain with the Neumann or periodic boundary conditions. This system is proposed as a conceptual model for cell polarity. Since the system has conservation of mass, the steady state problem is reduced to that of a scalar reaction–diffusion equation with a nonlocal term. That is, there is a one-to-one correspondence between an equilibrium solution of the system with a fixed mass and a solution of the scalar equation. In particular, we consider the case when the reaction term is linear in one variable. Then the equations are transformed into the same equations as the phase-field model for solidification. We thereby show that the equations allow a Lyapunov function. Moreover, by investigating the linearized stability of a nonconstant equilibrium solution, we prove that given a nondegenerate stable equilibrium solution of the nonlocal scalar equation, the corresponding equilibrium solution of the system is stable. We also exhibit global bifurcation diagrams for equilibrium solutions to specific model equations by numerics together with a normal form near a bifurcation point.