New noise‐to‐state stability and instability criteria for random nonlinear systems

2019 ◽  
Vol 30 (2) ◽  
pp. 526-537 ◽  
Author(s):  
Liqiang Yao ◽  
Weihai Zhang
Keyword(s):  
Nonlinear Systems ◽  
Instability Criteria ◽  
Stability And Instability

scholarly journals The complexity paradigm in management reconceptualizing

2005 ◽  
Vol 50 (167) ◽  
pp. 107-139
Author(s):  
Slavica Petrovic
Keyword(s):  
Nonlinear Systems ◽  
Complexity Theory ◽  
Systems Approach ◽  
Full Potential ◽  
Complex Dynamic ◽  
Edge Of Chaos ◽  
Order And Disorder ◽  
Stability And Instability ◽  
Creative Research ◽  
Creativity And Innovation

Chaos and complexity theory is a special, functionalist systems approach to dealing with complex, dynamic, nonlinear systems. Through treating organizations as complex, with their environments coevolving, nonlinear systems, complexity theory is aimed at creative research of their erratic nature. When an organization is in a state of bounded instability, at the edge of chaos, order and disorder are intertwined, its behavior is irregular and unpredictable but has some pattern. According to the complexity paradigm organizations have to strive to avoid the equilibrium states of stability and instability. They have instead to strive to remain in a state of bounded instability, at the edge of chaos, where they are able to display their full potential for creativity and innovation.

Frequency-domain instability criteria for time-varying and nonlinear systems

1967 ◽  
Vol 55 (5) ◽  
pp. 604-619 ◽  
Author(s):  
R.W. Brockett ◽  
H.B. Lee
Keyword(s):  
Nonlinear Systems ◽  
Frequency Domain ◽  
Time Varying ◽  
Instability Criteria

Stability of a Pin-Ended Bar in Torsion and Compression

1973 ◽  
Vol 40 (2) ◽  
pp. 405-410 ◽  
Author(s):  
J. A. Walker
Keyword(s):  
Direct Method ◽  
System Parameters ◽  
Torque Vector ◽  
Instability Criteria ◽  
Stability And Instability ◽  
Liapunov Functionals ◽  
The Stability

The stability of a uniform pin-ended bar having equal principal stiffnesses, subjected to combined torsion and compression, is studied via the direct method of Liapunov for cases in which the torque vector is circulatory; i.e., the torque vector does not bisect the angle between the undeformed and deformed axes of the bar. Liapunov functionals are presented and applied to both the case of a viscous environment and the case of a viscoelastic environment. Several simple stability and instability criteria are obtained in terms of the system parameters.

scholarly journals On the stability and instability criteria for circulatory systems: A review

2020 ◽  
pp. 13-13
Author(s):  
Ranislav Bulatovic
Keyword(s):  
Mechanical Systems ◽  
Numerical Examples ◽  
Instability Criteria ◽  
Stability And Instability ◽  
The Stability

A survey of the selected published criteria - expressed by the properties of the system matrices - for the stability and instability of linear mechanical systems subjected to potential and circulatory forces is presented. In particular, recent generalizations of the well-known Merkin instability theorem are reported. Several simple numerical examples are used to illustrate the usefulness of the presented criteria and also to compare them.

scholarly journals Robust Stability and Instability of Uncertain Nonlinear Systems with Uncertainty-dependent Equilibrium

2014 ◽  
Vol 50 (5) ◽  
pp. 387-394
Author(s):  
Takayuki ARAI ◽  
Masaki INOUE ◽  
Jun-Ichi IMURA ◽  
Kenji KASHIMA ◽  
Kazuyuki AIHARA
Keyword(s):  
Nonlinear Systems ◽  
Robust Stability ◽  
Uncertain Nonlinear Systems ◽  
Stability And Instability

Finite-time stability and instability of stochastic nonlinear systems

Automatica ◽  
2011 ◽  
Vol 47 (12) ◽  
pp. 2671-2677 ◽  
Author(s):  
Juliang Yin ◽  
Suiyang Khoo ◽  
Zhihong Man ◽  
Xinghuo Yu
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Stochastic Nonlinear Systems ◽  
Time Stability ◽  
Finite Time Stability ◽  
Stability And Instability

scholarly journals Dynamics of coupled nonlinear systems

2019 ◽  
Keyword(s):  
Nonlinear Systems ◽  
Total Energy ◽  
Fiber Optics ◽  
Degrees Of Freedom ◽  
Integrals Of Motion ◽  
Dynamical Equations ◽  
Magnetic Layers ◽  
Stability And Instability ◽  
Energy Integrals ◽  
Average Distribution

Two models were studied theoretically which describe the dynamics of two nonlinear elements with linear and nonlinear interaction between them. These models correspond to the commutators in nonlinear fiber optics and artificial lattices of magnetic nanodots or magnetic layers in quasi-two dimensional compounds. The models illustrate the common situation in the nonlinear systems with two degrees of freedom. Usually the absence of additional to the total energy integrals of motion leads to the appearance of a chaotic component of the dynamics. This chaotic behaviour masks the reqular part of the total dynamics. In the studied in the paper two integrable systems the chaotic component is absent and the reqular dynamics manifest itself per se. In the paper at first the dynamics of the systems was investigated qualitatively in the corresponding phase planes. Two integrals of motion correspond to the total energy E and the number N of elementary excitations in the system (photons and spin deviations). The phase analysis demonstrates the complicated its dynamics. The excitations of different types are classified in the plane of the integrals N,E . For the fix number of excitations N in the domain of small N the dynamics is close to the linear one and divides into two regions for quasi-inphase and quasi-antiphase oscillations. But for the large level of the excitation after the definite value of N N b  in the bifurcation way the region of another dynamics appears. For N N b  the minimum of the energy corresponds to the essentially nonlinear regime with nonunifor average distribution of the energy between two oscillators. At the same time the critical point which correspond to the in-phase oscillations transforms into saddle one and in-phase regime becomes unstable. As integrable the studied systems allow the solutions in the quadratures. The exact solution of the dynamical equations for nonlinear dynamics were obtained and analysed. The main result consists in the above prediction of the nonuniform states with different energies of subsystems, their stability and instability of inphase oscillations. The nonuniform states corresponds to the solitonic excitations in the systems with distributed parameters.

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