TUNING CHAOS SYNCHRONIZATION AND ANTI-SYNCHRONIZATION FOR APPLICATIONS IN TEMPORAL PATTERN RECOGNITION

2005 ◽  
Vol 15 (12) ◽  
pp. 3905-3921 ◽  
Author(s):  
OSCAR DE FEO

Various forms of chaotic synchronization have been proposed as ways of implementing associative memories and/or pattern recognizers. Within this context, a single chaotic dynamical system can be adopted as an implicit model of a whole class of approximately periodic signals [De Feo, 2003]. Then, by exploiting the selective properties of the recently illustrated phenomenon of Qualitative Resonance [De Feo, 2004a, 2004b], this model can be employed within a feedback-synchronization-based pattern recognition scheme. To this end, to exploit the qualitative resonance phenomenon in concrete applications, the synchronization feedback loop must be opportunely tuned. Namely, an approximately periodic pattern must regularize or reinforce the chaotic behavior of the whole system depending on whether it belongs to the class modeled by the chaotic model or not. Despite being apparently complicated, as shown here, the tuning of the synchronization feedback loop can be operated relying on standard methods from linear periodic control theory.

2005 ◽  
Vol 15 (10) ◽  
pp. 3345-3357 ◽  
Author(s):  
OSCAR DE FEO

Various forms of chaotic synchronization have been proposed as ways of realizing associative memories and/or pattern recognizers. To exploit this kind of synchronization phenomena in temporal pattern recognition, a chaotic dynamical system representing the class of signals that are to be recognized must be established. As shown recently [De Feo, 2003], this system can be determined by means of identification techniques where chaos emerges by itself to model the diversity of nearly periodic signals. However, the emerging chaotic behavior is subharmonic, i.e. period doubling-like, and therefore, as explained in [De Feo, 2004a, 2004b], it is not suitable for a synchronization-based pattern recognition technique. Nevertheless, as shown here, bifurcation theory and continuation techniques can be combined to modify a subharmonic chaotic system and drive it to homoclinic conditions; obtaining in this way a model suitable for synchronization-based pattern recognition.


2018 ◽  
Vol 6 (3) ◽  
pp. 107 ◽  
Author(s):  
Jean-Louis Pinault

Evidence of long-term variability in the upper ocean has emerged for two decades. Most of the issues discussed raise a lot of questions. What is the driver of the decadal oscillation of rainfall in Europe that has been observed since the end of the 20th century? How to explain low-frequency variability as observed in the Atlantic Multidecadal Oscillation (AMO)? More generally, how does solar and orbital forcing occur during very long-term climate change? The observations suggest that both a positive feedback loop amplifies the effects of the insolation gradient on the climate system and a resonance phenomenon occurs, filtering out some frequencies in favour of others. Throughout this paper, some answers to these problems are given from a new concept based on the modulated response of subtropical gyres to solar and orbital forcing. Subtropical gyres turn out to be the main driver of long-term climate variability because they tightly control, via the western boundary currents, heat transport from the tropics into middle and high latitudes. Specifically, the theoretical foundations of long-period Rossby waves winding around the subtropical gyres are laid, suggested by the observations of persistent sea surface temperature anomalies at mid-latitudes. Multi-frequency Gyral Rossby Waves (GRWs) exhibit properties resulting from their annular structure and their coupling. Using a β-cone approximation, the momentum equations are solved in polar coordinates. The gradient β of the Coriolis parameter depends on the mean radius of the annulus and remains constant all around the latter. GRWs result from the variation in the Coriolis Effect with the mean radius of the annulus. The speed of the anti-cyclonically wind-driven circulation being higher than the phase velocity of cyclonically propagating GRWs, amplified forcing effects occur as well as resonances for periods consistent with the observations.


2020 ◽  
Author(s):  
Lisa Tannock ◽  
Marco Herwegh ◽  
Alfons Berger ◽  
Klaus Regenauer-Lieb

<p>A paleohydrothermal giant quartz reef (at least 75 m wide, 40 km long) and abundant hot springs at the Heyuan fault, South China, provide an excellent opportunity to investigate hydrothermal flows from the Mesozoic through to present-day.</p><p>The giant quartz reef has formed in the extensional regime initiated in the Mesozoic, while a change to  compressional stress on the Heyuan in the Cenozoic led to the development of cross-cutting strike-slip faults and associated vertical fracture network. Here, we present multiscale observations and analyses from the earlier long-term extensional phase.</p><p>Detailed microstructural analyses identified a 'quartz-reef window' of formation occurring between ~200-350˚C, linking in both quasi-static criteria (accommodation space; massive fluid sources; and a cap rock/seal)  and dynamic mechanisms (episodic-dynamic permeability; brittle-ductile cycles; and fluid injection though brittle-ductile equivalent of Sibson's 'fault-valve' behaviour.</p><p>This oscillatory brittle-ductile fault-valve is recorded in the field through its apparent contradiction between idiomorphic 5 cm long quartz crystal growth in mode-I fractures, embedded at large-scale inside far from equilibrium fault zones with mylonitic and cataclastic microstructures. Another characteristic feature is the increasing quartz vein frequency towards the core shown by enrichment of SiO<sub>2</sub>, with depletion of K<sub>2</sub>O and  Na<sub>2</sub>O in tectonites during alteration from the host granite; a reaction partly sourcing the SiO<sub>2</sub> for the quartz reef.<br><br>We present a first theoretical model compatible with the observation of oscillatory macroscale far from equilibrium conditions, followed by long periods of micro-scale local equilibrium. The model can in particular describe mechanisms of abundant SiO<sub>2</sub> dominated fluid release reaching episodically above hydrostatic pressures followed by long periods of SiO<sub>2</sub> precipitation, allowing growth of up to 5 cm long idiomorphic quartz  crystals in subparallel open channels, which presumably were held open by high fluid pressures. In this interpretation, the observations instabilities are seen to stem from the multiscale and multiphysics of the mineral reactions at the brittle-ductile transition, promoted by a slow extensional geodynamic driver at the Heyuan fault.<br><br>The new approach allows interpretation of rock physics properties in terms of recently discovered Thermo-Hydro-Mechanical-Chemical (THMC) multiscale wave-like instabilities. In the model short wavelength chemical dissolution-precipitation reaction waves are bouncing between the phyllonitic cap rock and the mylonitic shear zone below. A resonance phenomenon of constructive interference in a finite width around the future quartz-reef triggers the long-time scale steady-state attractor allowing quartz reef growth over geodynamic time scales. We show that this solitary wave limit forms a standing wave matching the characteristic periodic pattern of mode-I quartz veining around the reef and also explaining the fluid overpressures leading to local hydro-fracturing.</p>


2021 ◽  
Vol 11 (2) ◽  
pp. 788
Author(s):  
Aceng Sambas ◽  
Sundarapandian Vaidyanathan ◽  
Talal Bonny ◽  
Sen Zhang ◽  
Sukono ◽  
...  

This paper starts with a review of three-dimensional chaotic dynamical systems equipped with special curves of balance points. We also propose the mathematical model of a new three-dimensional chaotic system equipped with a closed butterfly-like curve of balance points. By performing a bifurcation study of the new system, we analyze intrinsic properties such as chaoticity, multi-stability, and transient chaos. Finally, we carry out a realization of the new multi-stable chaotic model using Field-Programmable Gate Array (FPGA).


2019 ◽  
Vol 4 (2) ◽  
pp. 315-330 ◽  
Author(s):  
Sk. Sarif Hassan ◽  
Moole Parameswar Reddy ◽  
Ranjeet Kumar Rout

AbstractThe Lorenz model is one of the most studied dynamical systems. Chaotic dynamics of several modified models of the classical Lorenz system are studied. In this article, a new chaotic model is introduced and studied computationally. By finding the fixed points, the eigenvalues of the Jacobian, and the Lyapunov exponents. Transition from convergence behavior to the periodic behavior (limit cycle) are observed by varying the degree of the system. Also transiting from periodic behavior to the chaotic behavior are seen by changing the degree of the system.


2016 ◽  
Vol 26 (05) ◽  
pp. 1650080 ◽  
Author(s):  
K. L. Joiner ◽  
F. Palmero ◽  
R. Carretero-González

The nonlinear dynamics of an optoelectronic negative feedback switching circuit is studied. The circuit, composed of a bulb, a photoresistor, a thyristor and a linear resistor, corresponds to a nightlight device whose light is looped back into its light sensor. Periodic bifurcations and deterministic chaos are obtained by the feedback loop created when the thyristor switches on the bulb in the absence of light being detected by the photoresistor and the bulb light is then looped back into the nightlight to switch it off. The experimental signal is analyzed using tools of delay-embedding reconstruction that yield a reconstructed attractor with fractional dimension and positive Lyapunov exponent suggesting chaotic behavior for some parameter values. We construct a simple circuit model reproducing experimental results that qualitatively matches the different dynamical regimes of the experimental apparatus. In particular, we observe an order-chaos-order transition as the strength of the feedback is varied corresponding to varying the distance between the nightlight bulb and its photo-detector. A two-dimensional parameter diagram of the model reveals that the order-chaos-order transition is generic for this system.


2004 ◽  
Vol 14 (03) ◽  
pp. 893-912 ◽  
Author(s):  
OSCAR DE FEO

This is the second of two papers introducing a new dynamical phenomenon, strongly related to the problems of synchronization and control of chaotic dynamical systems, and presenting the corresponding mathematical analysis, conducted both experimentally and theoretically. In particular, it is shown that different dynamical models (ordinary differential equations) admitting chaotic behavior organized by a homoclinic bifurcation to a saddle-focus (Shil'nikov-like chaos) tend to have a particular selective property when externally perturbed. Namely, these systems settle on a very narrow chaotic behavior, which is strongly correlated to the forcing signal, when they are slightly perturbed with an external signal which is similar to their corresponding generating cycle. Here, the "generating cycle" is understood to be the saddle cycle colliding with the equilibrium at the homoclinic bifurcation. On the other hand, when they are slightly perturbed with a generic signal, which has no particular correlation with their generating cycle, their chaotic behavior is reinforced. This peculiar behavior has been called qualitative resonance underlining the fact that such chaotic systems tend to resonate with signals that are qualitatively similar to an observable of their corresponding generating cycle. Here, a detailed mathematical analysis of the qualitative resonance phenomenon is presented, confirming the intuitions given by the geometrical model discussed in Part I.


2004 ◽  
Vol 14 (08) ◽  
pp. 2867-2873 ◽  
Author(s):  
KEN KIERS ◽  
TIM KLEIN ◽  
JEFF KOLB ◽  
STEVE PRICE ◽  
J. C. SPROTT

We explore the chaotic behavior of a nonlinear electrical circuit constructed with simple components such as diodes and linear operational amplifiers. The circuit may be regarded as a nonlinear analog computer that gives a nearly exact solution of a particular chaotic model. Detailed comparisons between theoretical and experimental bifurcation points and power spectra yield differences of less than 1%.


2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Zhenyu Lu ◽  
Tingya Yang ◽  
Min Zhu

Recently, the stochastic resonance effect has been widely used by the method of discovering and extracting weak periodic signals from strong noise through the stochastic resonance effect. The detection of the single-frequency weak signals by using stochastic resonance effect is widely used. However, the detection methods of the multifrequency weak signals need to be researched. According to the different frequency input signals of a given system, this paper puts forward a detection method of multifrequency signal by using adaptive stochastic resonance, which analyzed the frequency characteristics and the parallel number of the input signals, adjusted system parameters automatically to the low frequency signals in the fixed step size, and then measured the stochastic resonance phenomenon based on the frequency of the periodic signals to select the most appropriate indicators in the middle or high frequency. Finally, the optimized system parameters are founded and the frequency of the given signals is extracted in the frequency domain of the stochastic resonance output signals. Compared with the traditional detection methods, the method in this paper not only improves the work efficiency but also makes it more accurate by using the color noise, the frequency is more accurate being extracted from the measured signal. The consistency between the simulation results and analysis shows that this method is effective and feasible.


Sign in / Sign up

Export Citation Format

Share Document