Although the problem of locked-in deep stall is well documented over many years, there currently exists no consistent procedure that can guarantee recovery. Past studies have suggested that it might be possible to rock the aircraft in pitch to destabilise the statically stable deep stall trim point, thereby gaining enough momentum to push the nose down. However, the methods used in these studies are either of preliminary or empirical nature and cannot guarantee recovery. In this paper, we use bifurcation analysis to derive a recovery manoeuvre, specifically by assessing the aircraft’s nonlinear frequency response under an elevator forcing. The ensuing nonlinear Bode plot detects unstable (divergent) solutions near resonance that contribute to a successful deep stall recovery. Moreover, the nonlinear resonant frequency is slightly lower than the result obtained using linear analysis, and time simulation shows that relying on the linear result does not lead to a successful recovery. It is also found that at the high angles of attack associated with deep stall, the frequency separation between the short period and phugoid mode is significantly reduced, leading to only one visible peak in the frequency response. This feature is also reflected in the time-domain step response.

This paper is concerned with a prey–predator model with population flux by attractive transition. Our previous paper (Oeda and Kuto, 2018, Nonlinear Anal. RWA, 44, 589–615) obtained a bifurcation branch (connected set) of coexistence steady states which connects two semitrivial solutions. In Oeda and Kuto (2018, Nonlinear Anal. RWA, 44, 589–615), we also showed that any positive steady-state approaches a positive solution of either of two limiting systems, and moreover, one of the limiting systems is an equal diffusive competition model. This paper obtains the bifurcation structure of positive solutions to the other limiting system. Moreover, this paper implies that the global bifurcation branch of coexistence states consists of two parts, one of which is a simple curve running in a tubular domain near the set of positive solutions to the equal diffusive competition model, the other of which is a connected set characterized by positive solutions to the other limiting system.

This paper analyzes the dynamical properties of monetary models with regime switching. We start with the analysis of the evolution of inflation when policy is guided by a simple monetary rule where coefficients switch with the policy regime. We rule out the possibility of a Hopf bifurcation and demonstrate the possibility of a period-doubling bifurcation. As a result, a small change in the parameters (e.g., a more active policy response) can lead to a drastic change in the path of inflation. We show that the New Keynesian model with a current-looking Taylor rule is not prone to bifurcations. A New Keynesian model with a hybrid rule, however, exhibits the same pattern of period-doubling bifurcations as the analysis with a simple monetary rule.

We are interested in the stability of the localized stationary solutions of a three-component reaction-diffusion system with one activator and two inhibitors. We show that depending on control parameters, solutions in form of moving and breathing localized structures can be observed in the vicinity of the codimension-two bifurcation point. We analyze this situation performing multiple scale perturbation expansion in the vicinity of the bifurcation point and derive a set of order parameter equations, explicitly describing the dynamics of the single localized structure. Numerical simulations are carried out, showing good agreement with the analytical predictions.

We develop a framework for analysing the outcome of resource competition based onbifurcation theory. We elaborate our methodology by readdressing the problem ofcompetition of two species for two resources in a chemostat environment. In the case ofperfect-essential resources it has been extensively discussed using Tilman’srepresentation of resource quarter plane plots. Our mathematically rigorous analysisyields bifurcation diagrams with a striking similarity to Tilman’s method including theinterpretation of the consumption vector and the resource supply vector. However, ourapproach is not restricted to a particular class of models but also works with othertrophic interaction formulations. This is illustrated by the analysis of a modelconsidering interactively-essential or complementary resources instead ofprefect-essential resources. Additionally, our approach can also be used for otherecosystem compositions: multiple resources–multiple species communities with equilibriumor oscillatory dynamics. Hence, it gives not only a new interpretation of Tilman’sgraphical approach, but it constitutes an extension of competition analyses to communitieswith many species as well as non-equilibrium dynamics.

This paper studies the nature of long-run behavior in a two-sector model of optimal growth. Under some restrictions on the parameters of the model, we provide an explicit solution of the optimal policy function generated by the optimal growth model. Fixing the discount factor, we indicate how long-run optimal dynamics changes as a key technological parameter (labor output ratio) changes. For a particular configuration of parameter values, we also provide an explicit solution of the unique absolutely continuous invariant ergodic distribution generated by the optimal policy function.