## What is/are Dynamic Bifurcation?

Dynamic Bifurcation - In the course of the work, the stability limits for static and dynamic bifurcations were obtained with respect to many parameters of the system, including with respect to the value of the load conductivity.^{[1]}Our approach shows the rich static and dynamic bifurcation topology of the continuous fermentation reactor, which includes Fold, Hopf, Bautin, and Cusp bifurcations.

^{[2]}We demonstrate that the onset of the second solution, a nematodynamic bifurcation yielding energetically degenerate director tilts at the threshold pressure gradient, can be controlled by the surface anchoring and the flow driving mechanism (pressure-driven or volume-driven).

^{[3]}A dynamic bifurcation analysis on a three-species cooperating model was presented and it was proved that the problem bifurcated an attractor as the parameter λ crossed the critical value λ0.

^{[4]}In this work new global dynamic bifurcation theorems are established for local semiflows on complete metric spaces.

^{[5]}Hopf bifurcation, as the most representative dynamic bifurcation, is closely related to the stability of many engineering structures.

^{[6]}It is shown that, when the threshold in the heating intensity is exceeded, a dynamic bifurcation of the solution of the MHD system under consideration occurs, as a result of which the value of the average E × B drift velocity increases significantly.

^{[7]}Finally, the amplitude-frequency characteristics of the work roll under different external excitation amplitude and the dynamic bifurcation characteristics of the work roll under different gaps are analyzed.

^{[8]}It is revealed that the collective cell oscillation in an epithelium-like monolayer results from the dynamic bifurcation induced by negative feedback between mechanical strains and chemical cues.

^{[9]}The transition mechanism from mono-stability to multi-stability is deeply investigated by means of equilibrium bifurcation, potential well diagrams and dynamic bifurcation, respectively.

^{[10]}In this paper we present some local dynamic bifurcation results in terms of invariant sets of nonlinear evolution equations.

^{[11]}The effects of the mass ratio and stiffness ratio on the dynamic performances of the hybrid energy harvester are numerically investigated with dynamic bifurcation diagrams method.

^{[12]}This is done by a hierarchical recurrent neural learning framework (RNN) because of its nonlinear dynamic bifurcation, so that variables can be learned to represent different hierarchies.

^{[13]}We divide the pulse structure into regions that produce push and pull effects in the gel in order to gain insight into the modification of the asymmetric structure of the chemical waves that leads to spatiotemporal dynamic bifurcation.

^{[14]}In the observation of limit cycle oscillations (LCO) and evolution of dynamic bifurcation, aerodynamic nonlinearity produces a smaller amplitude response compared with linear piston theory, but has no apparent influence on dynamic bifurcation.

^{[15]}Amplitude sweeps are conducted showing a dynamic bifurcation point that varies as a function of frequency and effective damping.

^{[16]}Mechanism analysis was studied of bifurcated carbon nanotubes from chemical crystallization bifurcation and nonlinear dynamic bifurcation.

^{[17]}We analyze the effects of cavity parameters on the DSR-pulse features under the dynamic bifurcations.

^{[18]}A closed-form expression for the sensitivity of dynamic bifurcation sensors was derived.

^{[19]}This perspective views pathogen emergence and re-emergence as a “critical transition,” and uses the concept of noisy dynamic bifurcation to understand the relationship between the system observables and the distance to this transition.

^{[20]}An asymptotic solution near such a dynamic bifurcation is constructed.

^{[21]}The dynamic bifurcation of the LR3BP under angular velocity variation is obtained based on three typical kinds of periodic orbits, i.

^{[22]}Therefore, we propose dynamic bifurcation as a crucial built-in mechanism of macrophage polarization.

^{[23]}Moreover, in light of the nonlinear dynamic bifurcation theory, the system stability was analyzed by taking the resistance value of power motor as the bifurcation parameter.

^{[24]}The hysteresis loops are accurately distinguished from the dynamic bifurcation phenomenon that is related to the dynamic effect of slowly varying parameters.

^{[25]}At a certain flow velocity, the stability of tube array reaches the first critical state, a dynamic bifurcation occurs.

^{[26]}

## Nonlinear Dynamic Bifurcation

This is done by a hierarchical recurrent neural learning framework (RNN) because of its nonlinear dynamic bifurcation, so that variables can be learned to represent different hierarchies.^{[1]}Mechanism analysis was studied of bifurcated carbon nanotubes from chemical crystallization bifurcation and nonlinear dynamic bifurcation.

^{[2]}Moreover, in light of the nonlinear dynamic bifurcation theory, the system stability was analyzed by taking the resistance value of power motor as the bifurcation parameter.

^{[3]}