Abstract The main purpose of this paper is to build a family tutorial Goodwinian (essentially Marxist) models capital accumulation through industrial cycles that are less complicated than the author’s extended capitalist reproduction in USA already published. subordinate advance refinement these from standard “neoclassical” assumptions distort generic structures determining perpetual disequilib...

Bursting behavior in neurons is a recurrent transition between a quiescent state and repetitive spiking. When the transition to repetitive spiking occurs via a subcritical Andronov–Hopf bifurcation and the transition to the quiescent state occurs via double limit cycle bifurcation, the burster is said to be of subcritical elliptic type. When the fast subsystem is near a Bautin (generalized Hopf...

The solution manifold of the system of nonlinear differential equations representing a BWR needs to be examined to understand its dynamical behavior. In particular, stable or unstable fixed points and stable or unstable oscillatory solutions (or turning points/saddle node bifurcations) are of paramount interest. In this framework integrated BWR (system) codes and simplified BWR models (reduced ...

An extended reduced order model is presented and applied to analyze global and regional oscillations in BWRs. Stability and semianalytical bifurcation analyses are performed using this model in conjunction with the bifurcation code BIFDD to determine the stability limits for both in-phase and out-of-phase oscillation modes and the nature of Poincaré–Andronov–Hopf bifurcation. The results obtain...

ABSTRACT Prediction of brake squeal as unwanted high frequency noise above 1 kHz remains a challenging problem despite substantial research efforts in the past two decades. Brake squeal, triggered by friction-induced self-excited vibration, can be caused by many different and interacting mechanisms with nonlinear origins in material properties and boundary conditions. Although brake squeal is e...

The neocortex of the brain plays a most important role in achieving functions via electrical activities neurons. Understanding transition regularity firing patterns and underlying dynamics neurons can help to identify treat some diseases. Different neocortical exhibit regular spiking (RS), fast (FS), intrinsic bursting (IB), continuous (CB), which play vital roles wide range functions. Fast-slo...

We extend the formulae given by Azé–Corvellec, Belousov–Andronov and Ng–Zheng for the Hoffman constant associated to the system of linear inequalities Ax ≤ b and relate them to that established by Li.

Homoclinic bifurcations in autonomous ordinaty differential equations provide useful organizing centres for the analysis of examples. There are four generic types of homoclinic bifurcation, depending on the dominant eigenvalues of the Jacobian matrix of the flow near a stationary point. A family of differential equations is presented which, for suitable choices of parameters, can exhibit each o...