Frequency locking and complex dynamics near a periodically forced robust heteroclinic cycle

2006 ◽  
Vol 74 (5) ◽  
Author(s):  
J. H. P. Dawes ◽  
T. L. Tsai
Keyword(s):  
Complex Dynamics ◽  
Heteroclinic Cycle ◽  
Frequency Locking

Complex Dynamics of a Four-Dimensional Circuit System

2021 ◽  
Vol 31 (14) ◽  
Author(s):  
Haijun Wang ◽  
Hongdan Fan ◽  
Jun Pan
Keyword(s):  
Complex Dynamics ◽  
Numerical Technique ◽  
Heteroclinic Orbit ◽  
Pitchfork Bifurcation ◽  
Heteroclinic Orbits ◽  
Heteroclinic Cycle ◽  
Stable Node ◽  
Geometrical Structures ◽  
Heteroclinic Cycles ◽  
Forming Mechanism

Combining qualitative analysis and numerical technique, the present work revisits a four-dimensional circuit system in [Ma et al., 2016] and mainly reveals some of its rich dynamics not yet investigated: pitchfork bifurcation, Hopf bifurcation, singularly degenerate heteroclinic cycle, globally exponentially attractive set, invariant algebraic surface and heteroclinic orbit. The main contributions of the work are summarized as follows: Firstly, it is proved that there exists a globally exponentially attractive set with three different exponential rates by constructing a suitable Lyapunov function. Secondly, the existence of a pair of heteroclinic orbits is also proved by utilizing two different Lyapunov functions. Finally, numerical simulations not only are consistent with theoretical results, but also illustrate potential existence of hidden attractors in its Lorenz-type subsystem, singularly degenerate heteroclinic cycles with distinct geometrical structures and nearby hyperchaotic attractors in the case of small [Formula: see text], i.e. hyperchaotic attractors and nearby pseudo singularly degenerate heteroclinic cycles, i.e. a short-duration transient of singularly degenerate heteroclinic cycles approaching infinity, or the true ones consisting of normally hyperbolic saddle-foci (or saddle-nodes) and stable node-foci, giving some kind of forming mechanism of hyperchaos.

ANALYTICAL APPROXIMATION OF HETEROCLINIC BIFURCATION IN A 1:4 RESONANCE

2012 ◽  
Vol 22 (12) ◽  
pp. 1250294 ◽  
Author(s):  
ABDELHAK FAHSI ◽  
MOHAMED BELHAQ
Keyword(s):  
Limit Cycle ◽  
Analytical Approach ◽  
Analytical Approximation ◽  
Heteroclinic Cycle ◽  
Slow Flow ◽  
Heteroclinic Bifurcation ◽  
Subharmonic Solution ◽  
Frequency Locking ◽  
Flow Limit ◽  
Forced Oscillator

Bifurcation of heteroclinic cycle near 1:4 resonance in a self-excited parametrically forced oscillator with quadratic nonlinearity is investigated analytically in this paper. This bifurcation mechanism leads to the disappearance of a slow flow limit cycle giving rise to frequency-locking near the resonance. The analytical approach used to approximate the bifurcation is based on a collision criterion between the slow flow limit cycle and saddles involved in the bifurcation. The amplitudes of the 1:4-subharmonic solution and the slow flow limit cycle are approximated using a double perturbation procedure and the heteroclinic bifurcation is captured applying the collision criterion. For validation, the analytical results are compared to those obtained by numerical simulations.

Frontiers in Complex Dynamics

2014 ◽  
Author(s):  
Araceli Bonifant ◽  
Misha Lyubich ◽  
Scott Sutherland
Keyword(s):  
Historical Perspective ◽  
Complex Dynamics ◽  
Short Paper ◽  
Combinatorial Group Theory ◽  
Entropy Theory ◽  
Holomorphic Dynamics ◽  
Eightieth Birthday ◽  
Several Variables ◽  
Fields Medal ◽  
Combinatorial Group

John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P. Steele prizes. In honor of his eightieth birthday, this book gathers together surveys and papers inspired by Milnor's work, from distinguished experts examining not only holomorphic dynamics in one and several variables, but also differential geometry, entropy theory, and combinatorial group theory. The book contains the last paper written by William Thurston, as well as a short paper by John Milnor himself. Introductory sections put the papers in mathematical and historical perspective, color figures are included, and an index facilitates browsing.

An Alternative Approach To User Fee Policy In The Primary Health Care Setting Of Bangladesh.

2020 ◽  
Author(s):  
Nazneen Akhter
Keyword(s):  
Health Care ◽  
Primary Health Care ◽  
Complex Dynamics ◽  
Quality Care ◽  
Secondary Data ◽  
User Fees ◽  
Primary Health ◽  
Alternative Approach ◽  
Benefit Principle ◽  
User Fee

The concept of ascribing user fee in health care settings always remained a policy struggle and countries experienced different learning in this regards while implementing user fee at different tiers of health settings. The most exquisite learning among the many country specific evidences related to user fee are the match and mismatch between the equity principle and benefit principle while considering the client perspective. There is an added dimension of quality care which also add more complex dynamics into this concept since the quality care consideration has a double edged perspective both for clients and providers, where which one will get superiority over whom is a great question in health care, especially in the Primary Health care (PHC) of the country. In this reality the appropriate implementation guideline, followed by an appropriate practice of the administrative and management both service oriented and financial are of great importance in this user fee implementation consideration which always remained a challenge in the health care specially in remote care of PHC. This paper attempted a secondary data searching and scoping the available documents of Bangladesh and across the world to find an alternative approach to user fees policy where equity and benefit principle and quality - these three have to be placed in a well-constructed triad in PHC implementation which has been recommended as an alternative policy imperative in approaching user fees for Bangladesh PHC settings.

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