"Study of effect of the inductor on dynamical behavior for electronic circuit by using nonlinear part from type memductance

"The effect of the coil on the dynamical behavior of the electronic circuit with nonlinear part memductance was studied, where we studied four coil values: L = 90mH, L = 80mH, L = 70mH and L = 100mH with changing the value of the first capacitance c1. We obtained stability maps consisting of two regions (the dynamical behavior zone and the stability zone), where the dividing line is the Hopf bifurcation line, as well as the bifurcation diagram for each value from the coil and the first capacitance was obtained, as well as the phase portrait diagram in which we obtained the chaotic attractions And the period of the first, second, third, fourth, fifth, sixth and eighth.

Effects of Initial Stress Field and Critical Slip-Weakening Distance on Rupture Selectivity of 3D Buried Branched Faults

ABSTRACT Using the boundary integral equation method with the slip-weakening friction law, we investigate the effects of the initial stress field and the critical slip-weakening distance on the rupture selectivity on the 3D buried branched faults. The numerical results show that after reaching the bifurcation line between the main fault and the branched faults, rupture continues to propagate on one or both bifurcation planes (BPs), with rupture on one plane more favorable than the other. The initial stress distribution plays a decisive role in the selection of the favorable BP (FBP), and there is a critical status of stress distribution, around which rupture propagates on both planes, whereas the FBP switches between the two. For a given fault geometry, the critical status of initial stress, which is described by a ratio Fp between normal stresses, is related to the critical slip-weakening distance Dc.

Anomalous dynamics of active mode-locking in ring lasers with semiconductor optic amplifiers

The pulses development dynamics, including their bifurcation into two-pulse complexes, was investigated in ring semiconductor lasers with amplitude modulation, operating on harmonics. New unusual properties of active mode-locking were revealed. They indicate significantly different dynamics of lasers operating on the first harmonic and those operating on any higher harmonic. The domain of control parameters for single pulses of higher harmonics is split into two domains: the dynamic boundary layer of finite width adjacent to the bifurcation line and the domain of dynamic chaos. Such layers engender stable dynamic sync-bands. We found conditions to implement energy-efficient sync-bands with optimum pulse parameters.

Dynamic Viscoelastic Rod Stability Modeling by Fractional Differential Operator

The need to take into account the oscillation of a system is a special feature in the linear problem of the stability of a cantilevered rod under a follower force. Involvement of viscoelastic materials leads to damping of the oscillation hence to overestimation of critical loads. This new problem is solved here by means of an additional term introduced into the constitutive equation and proportional to the fractional time derivative with complex order—besides the inertial one. The effects contributed by the damping ratio, the real part of the order and the corrective role of its imaginary part on the shape of the bifurcation line, on its maximum and on the disposition of the inflection and maximal deflection points on the centerline of the deformed rod during the secondary loss of stability, are discussed.

When leisure becomes excessive: a bifurcation result in endogenous growth theory

The traditional assumption concerning endogenous labor supply in models of economic growth is that utility increases with leisure, independently of the specific time allocation of the representative agent observed at a given moment. In this note, we explore the consequences, over dynamic stability, of assuming that the agent dislikes having free time in excess, i.e., of considering that the marginal utility of leisure is not necessarily positive for every value of the leisure share (in particular, for high values of this share). By including this assumption in a typical AK endogenous growth model, we find that the system will rest, independently of parameter values, on a bifurcation line.