scholarly journals Spatiotemporal Organization of Correlated Local Activity within Global Avalanches in Slowly Driven Interfaces

2018 ◽  
Vol 121 (3) ◽  
Author(s):  
Ramon Planet ◽  
Juan M. López ◽  
Stéphane Santucci ◽  
Jordi Ortín
Keyword(s):  
Spatiotemporal Organization ◽  
Local Activity

scholarly journals Theorems and Application of Local Activity of CNN with Five State Variables and One Port

2012 ◽  
Vol 2012 ◽  
pp. 1-13
Author(s):  
Gang Xiong ◽  
Xisong Dong ◽  
Li Xie ◽  
Thomas Yang
Keyword(s):  
Bifurcation Diagram ◽  
Complex Dynamics ◽  
Nonlinear Dynamical Systems ◽  
Reaction Diffusion ◽  
Cellular Neural Network ◽  
State Variables ◽  
Nonlinear Dynamical ◽  
Local Activity ◽  
Homogeneous Lattice ◽  
Coupled Cells

Coupled nonlinear dynamical systems have been widely studied recently. However, the dynamical properties of these systems are difficult to deal with. The local activity of cellular neural network (CNN) has provided a powerful tool for studying the emergence of complex patterns in a homogeneous lattice, which is composed of coupled cells. In this paper, the analytical criteria for the local activity in reaction-diffusion CNN with five state variables and one port are presented, which consists of four theorems, including a serial of inequalities involving CNN parameters. These theorems can be used for calculating the bifurcation diagram to determine or analyze the emergence of complex dynamic patterns, such as chaos. As a case study, a reaction-diffusion CNN of hepatitis B Virus (HBV) mutation-selection model is analyzed and simulated, the bifurcation diagram is calculated. Using the diagram, numerical simulations of this CNN model provide reasonable explanations of complex mutant phenomena during therapy. Therefore, it is demonstrated that the local activity of CNN provides a practical tool for the complex dynamics study of some coupled nonlinear systems.

scholarly journals Motor Patterns During Walking on a Slippery Walkway

2010 ◽  
Vol 103 (2) ◽  
pp. 746-760 ◽  
Author(s):  
Germana Cappellini ◽  
Yuri P. Ivanenko ◽  
Nadia Dominici ◽  
Richard E. Poppele ◽  
Francesco Lacquaniti
Keyword(s):  
Motor Output ◽  
Emg Activity ◽  
Head Orientation ◽  
Cycle Duration ◽  
Horizontal Shear ◽  
Motor Patterns ◽  
Spatiotemporal Organization ◽  
Surface Conditions ◽  
Gait Kinematics ◽  
Slippery Surface

Friction and gravity represent two basic physical constraints of terrestrial locomotion that affect both motor patterns and the biomechanics of bipedal gait. To provide insights into the spatiotemporal organization of the motor output in connection with ground contact forces, we studied adaptation of human gait to steady low-friction conditions. Subjects walked along a slippery walkway (7 m long; friction coefficient ≃ 0.06) or a normal, nonslippery floor at a natural speed. We recorded gait kinematics, ground reaction forces, and bilateral electromyographic (EMG) activity of 16 leg and trunk muscles and we mapped the recorded EMG patterns onto the spinal cord in approximate rostrocaudal locations of the motoneuron (MN) pools to characterize the spatiotemporal organization of the motor output. The results revealed several idiosyncratic features of walking on the slippery surface. The step length, cycle duration, and horizontal shear forces were significantly smaller, the head orientation tended to be stabilized in space, whereas arm movements, trunk rotations, and lateral trunk inclinations considerably increased and foot motion and gait kinematics resembled those of a nonplantigrade gait. Furthermore, walking on the slippery surface required stabilization of the hip and of the center-of-body mass in the frontal plane, which significantly improved with practice. Motor patterns were characterized by an enhanced (roughly twofold) level of MN activity, substantial decoupling of anatomical synergists, and the absence of systematic displacements of the center of MN activity in the lumbosacral enlargement. Overall, the results show that when subjects are confronted with unsteady surface conditions, like the slippery floor, they adopt a gait mode that tends to keep the COM centered over the supporting limbs and to increase limb stiffness. We suggest that this behavior may represent a distinct gait mode that is particularly suited to uncertain surface conditions in general.

LOCAL ACTIVITY CRITERIA FOR DISCRETE-MAP CNN

2002 ◽  
Vol 12 (06) ◽  
pp. 1227-1272 ◽  
Author(s):  
VALERY I. SBITNEV ◽  
LEON O. CHUA
Keyword(s):  
Logistic Map ◽  
Period Doubling ◽  
Spiral Wave ◽  
Vortex Pinning ◽  
Magnetic Vortex ◽  
Critical Threshold ◽  
Local Activity ◽  
Cell Impedance ◽  
Initial Setting ◽  
Discrete Map

Discrete-time CNN systems are studied in this paper by the application of Chua's local activity principle. These systems are locally active everywhere except for one isolated parameter value. As a result, nonhomogeneous spatiotemporal patterns may be induced by any initial setting of the CNN system when the strength of the system diffusion coupling exceeds a critical threshold. The critical coupling coefficient can be derived from the loaded cell impedance of the CNN system. Three well-known 1D map CNN's (namely, the logistic map CNN, the magnetic vortex pinning map CNN, and the spiral wave reproducing map CNN) are introduced to illustrate the applications of the local activity principle. In addition, we use the cell impedance to demonstrate the period-doubling scenario in the logistic and the magnetic vortex pinning maps.

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