ON THE GENERATION OF SCROLL WAVES IN A THREE-DIMENSIONAL DISCRETE ACTIVE MEDIUM

1995 ◽  
Vol 05 (01) ◽  
pp. 313-320 ◽  
Author(s):  
LADISLAV PIVKA ◽  
ALEXANDER L. ZHELEZNYAK ◽  
CHAI WAH WU ◽  
LEON O. CHUA
Keyword(s):  
Neural Network ◽  
Active Medium ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Cellular Neural Network ◽  
Inhomogeneous Media ◽  
Wave Patterns ◽  
Scroll Wave ◽  
Scroll Waves

This paper reports on the simulation, in three-dimensional cellular-neural-network (CNN) arrays of Chua’s circuits, of basic three-dimensional scroll wave patterns observed previously from other media. Among the simulated patterns are the straight scroll wave, twisted scroll wave in both homogeneous and inhomogeneous media, as well as the scroll ring. These types of waves have been obtained for only one set of circuit parameters by varying the initial conditions.

Tension of organizing filaments of scroll waves

1994 ◽  
Vol 347 (1685) ◽  
pp. 611-630 ◽  
Keyword(s):  
Evolution Equation ◽  
Numerical Experiments ◽  
Asymptotic Theory ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Filament Length ◽  
Monotonic Change ◽  
Scroll Wave ◽  
Scroll Waves

We consider the asymptotic theory for the dynamics of organizing filaments of three-dimensional scroll waves. For a generic autowave medium where two dimensional vortices do not meander, we show that some of the coefficients of the evolution equation are always zero. This simpler evolution equation predicts a monotonic change of the total filament length with time, independently of initial conditions. Whether the filament will shrink or expand is determined by a single coefficient, the filament tension, that depends on the medium parameters. We illustrate the behaviour of scroll wave filaments with positive and negative tension by numerical experiments. In particular, we show that in the case of negative filament tension, the straight filament is unstable, and its evolution may lead to a multiplication of vortices.

scholarly journals Spiral waves within a bistability parameter region of an excitable medium

2022 ◽  
Author(s):  
Vladimir Zykov ◽  
Eberhard Bodenschatz
Keyword(s):  
Initial Conditions ◽  
Three Dimensional ◽  
Spiral Wave ◽  
Gradient Flow ◽  
Spiral Waves ◽  
Excitable Medium ◽  
Excitable Media ◽  
Circular Trajectory ◽  
Parameter Region ◽  
Scroll Wave

Abstract Spiral waves are a well-known and intensively studied dynamic phenomenon in excitable media of various types. Most studies have considered an excitable medium with a single stable resting state. However, spiral waves can be maintained in an excitable medium with bistability. Our calculations, performed using the widely used Barkley model, clearly show that spiral waves in the bistability region exhibit unique properties. For example, a spiral wave can either rotate around a core that is in an unexcited state, or the tip of the spiral wave describes a circular trajectory located inside an excited region. The boundaries of the parameter regions with positive and "negative" cores have been defined numerically and analytically evaluated. It is also shown that the creation of a positive or "negative" core may depend on the initial conditions, which leads to hysteresis of spiral waves. In addition, the influence of gradient flow on the dynamics of the spiral wave, which is related to the tension of the scroll wave filaments in a three-dimensional medium, is studied.

TWISTED SCROLL WAVES IN HETEROGENEOUS EXCITABLE MEDIA

1993 ◽  
Vol 03 (02) ◽  
pp. 445-450 ◽  
Author(s):  
ALEXANDER V. PANFILOV ◽  
JAMES P. KEENER
Keyword(s):  
Stationary Process ◽  
Three Dimensional ◽  
Excitable Medium ◽  
Excitable Media ◽  
Type Model ◽  
Refractory Periods ◽  
Scroll Wave ◽  
Scroll Waves

We study numerically the behavior of a scroll wave in a three-dimensional excitable medium with stepwise heterogeneity, using a FitzHugh Nagumo type model. We find that if the refractory periods in the two homogeneous subregions are sufficiently different, the scroll breaks into two scrolls rotating independently in each part of the medium. Eventually, the faster scroll eliminates the slower one leading to a stationary process, in which the scroll wave surviving in the region of faster recovery acts as a source for planar waves in the region of slower recovery.

scholarly journals Existence and Global Stability of a Periodic Solution for Discrete-Time Cellular Neural Networks

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Haijian Shao ◽  
Haikun Wei ◽  
Haoxiang Wang
Keyword(s):  
Neural Network ◽  
Periodic Solution ◽  
Global Stability ◽  
Discrete Time ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Lyapunov Stability Theory ◽  
Cellular Neural Network

A novel sufficient condition is developed to obtain the discrete-time analogues of cellular neural network (CNN) with periodic coefficients in the three-dimensional space. Existence and global stability of a periodic solution for the discrete-time cellular neural network (DT-CNN) are analysed by utilizing continuation theorem of coincidence degree theory and Lyapunov stability theory, respectively. In addition, an illustrative numerical example is presented to verify the effectiveness of the proposed results.

scholarly journals Application of CSK Encryption Algorithm in Video Synergic Command Systems

2022 ◽  
Vol 34 (2) ◽  
pp. 1-18
Author(s):  
Lele Qin ◽  
Guojuan Zhang ◽  
Li You
Keyword(s):  
Initial Conditions ◽  
Three Dimensional ◽  
Cellular Neural Network ◽  
Video Frame ◽  
Information Control ◽  
Network Access ◽  
Chen System ◽  
Protection Mechanism ◽  
Emergency Rescue ◽  
Control Command

Video command and dispatch systems have become essential communication safeguard measures in circumstances of emergency rescue, epidemic prevention, and control command as, data security has become especially important. After meeting the requirements of voice and video dispatch, this paper proposes an end-to-end encryption method of multimedia information that introduces a multiple protection mechanism including selective encryption and selective integrity protection. The method has a network access authentication and service encryption workflow, which implants startup authentication and key distribution into the information control signaling procedure. This method constitutes a key pool with the three-dimensional Lorenz System, the four-dimensional Cellular Neural Network (CNN) System and the four-dimensional Chen System where the key source system and initial conditions are decided by the plaintext video frame itself. Then, this method optimizes the chaotic sequences to further enhance system security.

Twisted scroll wave dynamics: partially pinned waves in excitable chemical media

2019 ◽  
Vol 21 (5) ◽  
pp. 2419-2425 ◽  
Author(s):  
Porramain Porjai ◽  
Malee Sutthiopad ◽  
Kritsana Khaothong ◽  
Metinee Phantu ◽  
Nakorn Kumchaiseemak ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Excitable Media ◽  
Wave Dynamics ◽  
Scroll Wave ◽  
Scroll Waves

We present an investigation of the dynamics of scroll waves that are partially pinned to inert cylindrical obstacles of varying lengths and diameters in three-dimensional Belousov–Zhabotinsky excitable media.

3-D CELLULAR NEURAL NETWORKS WITH CYCLIC CONNECTIONS CANNOT EXHIBIT CHAOS

2008 ◽  
Vol 18 (04) ◽  
pp. 1227-1230 ◽  
Author(s):  
XIAO-SONG YANG
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Three Dimensional ◽  
Cellular Neural Network ◽  
Cellular Neural Networks

In this letter we prove that every three-dimensional cellular neural network with cyclic connection does not support chaos.

scholarly journals VO2 Carbon Nanotube Composite Memristor-Based Cellular Neural Network Pattern Formation

Electronics ◽  
2021 ◽  
Vol 10 (10) ◽  
pp. 1198
Author(s):  
Yiran Shen ◽  
Guangyi Wang
Keyword(s):  
Neural Network ◽  
Carbon Nanotube ◽  
Complex Space ◽  
Initial Conditions ◽  
Processing System ◽  
Cellular Neural Network ◽  
Edge Of Chaos ◽  
Time Patterns ◽  
Carbon Nanotube Composite ◽  
Network Pattern

A cellular neural network (CNN) based on a VO2 carbon nanotube memristor is proposed in this paper. The device is modeled by SPICE at first, and then the cell dynamic characteristics based on the device are analyzed. It is pointed out that only when the cell is at the sharp edge of chaos can the cell be successfully awakened after the CNN is formed. In this paper, we give the example of a 5 × 5 CNN, set specific initial conditions and observe the formed pattern. Because the generated patterns are affected by the initial conditions, the cell power supply can be pre-programmed to obtain specific patterns, which can be applied to the future information processing system based on complex space–time patterns, especially in the field of computer vision.

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