Characteristics of Stick Regions in Frictional Vibration with a Compressed Nonlinear Spring

2006 ◽  
Vol 321-323 ◽  
pp. 1585-1588
Author(s):  
Ki Hong Shin ◽  
Young Sup Lee
Keyword(s):  
Compression Ratio ◽  
Stable Equilibrium ◽  
Equilibrium Points ◽  
Plane Motion ◽  
Multiple Equilibrium ◽  
Single Degree Of Freedom ◽  
Frictional System ◽  
Multiple Equilibrium Points ◽  
Stable Points ◽  
Frictional Vibration

In-plane characteristics of a single degree of freedom frictional system with a compressed spring are considered. The compressed spring is vertically installed to the mass moving horizontally along the friction interface. The compressed spring can introduce a nonlinear negative stiffness into the in-plane motion. The resulting system has a multiple equilibrium points; an unstable point at the center and two stable points on either side. It is shown that two stable equilibrium points can be separated far apart by increasing the compression ratio and the stiffness of the spring. The friction system is often characterized by stick and slip motions that cause unfavorable effects such as wear, noise, and chatter etc. It is demonstrated that increasing the compression ratio and the stiffness of the spring results in decreasing the size of the stick regions.

A new hyperchaotic particle motion system and its control

2019 ◽  
Vol 30 (12) ◽  
pp. 2050004
Author(s):  
Ning Cui ◽  
Junhong Li
Keyword(s):  
Particle Motion ◽  
Initial Conditions ◽  
Equilibrium Points ◽  
Multiple Equilibrium ◽  
Hopf Bifurcations ◽  
Hyperchaotic System ◽  
Motion System ◽  
The Rich ◽  
Theoretical Analyses ◽  
Multiple Equilibrium Points

This paper formulates a new hyperchaotic system for particle motion. The continuous dependence on initial conditions of the system’s solution and the equilibrium stability, bifurcation, energy function of the system are analyzed. The hyperchaotic behaviors in the motion of the particle on a horizontal smooth plane are also investigated. It shows that the rich dynamic behaviors of the system, including the degenerate Hopf bifurcations and nondegenerate Hopf bifurcations at multiple equilibrium points, the irregular variation of Hamiltonian energy, and the hyperchaotic attractors. These results generalize and improve some known results about the particle motion system. Furthermore, the constraint of hyperchaos control is obtained by applying Lagrange’s method and the constraint change the system from a hyperchaotic state to asymptotically state. The numerical simulations are carried out to verify theoretical analyses and to exhibit the rich hyperchaotic behaviors.

scholarly journals Multistability and Multiperiodicity for a General Class of Delayed Cohen-Grossberg Neural Networks with Discontinuous Activation Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Yanke Du ◽  
Yanlu Li ◽  
Rui Xu
Keyword(s):  
Neural Networks ◽  
Periodic Orbits ◽  
General Class ◽  
Equilibrium Points ◽  
Sufficient Conditions ◽  
Multiple Equilibrium ◽  
Activation Functions ◽  
Discontinuous Activation ◽  
Discontinuous Activation Functions ◽  
Multiple Equilibrium Points

A general class of Cohen-Grossberg neural networks with time-varying delays, distributed delays, and discontinuous activation functions is investigated. By partitioning the state space, employing analysis approach and Cauchy convergence principle, sufficient conditions are established for the existence and locally exponential stability of multiple equilibrium points and periodic orbits, which ensure thatn-dimensional Cohen-Grossberg neural networks withk-level discontinuous activation functions can haveknequilibrium points orknperiodic orbits. Finally, several examples are given to illustrate the feasibility of the obtained results.

scholarly journals Discontinuity Induced Hopf and Neimark–Sacker Bifurcations in a Memristive Murali–Lakshmanan–Chua Circuit

2017 ◽  
Vol 27 (06) ◽  
pp. 1730021 ◽  
Author(s):  
A. Ishaq Ahamed ◽  
M. Lakshmanan
Keyword(s):  
Floquet Theory ◽  
Equilibrium Points ◽  
Multiple Equilibrium ◽  
Hopf Bifurcations ◽  
Chua Circuit ◽  
Local Bifurcations ◽  
Generalized Differential ◽  
Multiple Equilibrium Points ◽  
Zero Time ◽  
Time Discontinuity

We report using Clarke’s concept of generalized differential and a modification of Floquet theory to nonsmooth oscillations, the occurrence of discontinuity induced Hopf bifurcations and Neimark–Sacker bifurcations leading to quasiperiodic attractors in a memristive Murali–Lakshmanan–Chua (memristive MLC) circuit. The above bifurcations arise because of the fact that a memristive MLC circuit is basically a nonsmooth system by virtue of having a memristive element as its nonlinearity. The switching and modulating properties of the memristor which we have considered endow the circuit with two discontinuity boundaries and multiple equilibrium points as well. As the Jacobian matrices about these equilibrium points are noninvertible, they are nonhyperbolic, some of these admit local bifurcations as well. Consequently when these equilibrium points are perturbed, they lose their stability giving rise to quasiperiodic orbits. The numerical simulations carried out by incorporating proper discontinuity mappings (DMs), such as the Poincaré discontinuity map (PDM) and zero time discontinuity map (ZDM), are found to agree well with experimental observations.

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