Nonlinear dynamics based digital logic and circuits

We discuss the role and importance of dynamics in the brain and biological neural networks and argue that dynamics is one of the main missing elements in conventional Boolean logic and circuits. We summarize a simple dynamics based computing method, and categorize different techniques that we have introduced to realize logic, functionality, and programmability. We discuss the role and importance of coupled dynamics in networks of biological excitable cells, and then review our simple coupled dynamics based method for computing. In this paper, for the first time, we show how dynamics can be used and programmed to implement computation in any given base, including but not limited to base two.

[1]  Haipeng Peng,et al.  Constructing Dynamic Multiple-Input Multiple-Output Logic Gates , 2011 .

[2]  J. W. Kim,et al.  Firing patterns in a conductance-based neuron model: bifurcation, phase diagram, and chaos , 2013, Biological Cybernetics.

[3]  Eric Campos-Cantón,et al.  A Simple Circuit with Dynamic Logic Architecture of Basic Logic Gates , 2010, Int. J. Bifurc. Chaos.

[4]  J. Martinerie,et al.  The brainweb: Phase synchronization and large-scale integration , 2001, Nature Reviews Neuroscience.

[5]  M. F. Shlesinger,et al.  The brain as a dynamic physical system , 1994, Neuroscience.

[6]  W L Ditto,et al.  Computing with distributed chaos. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  Sudeshna Sinha,et al.  Parallel computing with extended dynamical systems. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Pierre Collet,et al.  Concepts and Results in Chaotic Dynamics: A Short Course , 2006 .

[9]  Sudeshna Sinha,et al.  Introduction to focus issue: intrinsic and designed computation: information processing in dynamical systems--beyond the digital hegemony. , 2010, Chaos.

[10]  Jean-Jacques E. Slotine,et al.  Synchronization and Redundancy: Implications for Robustness of Neural Learning and Decision Making , 2010, Neural Computation.

[11]  W. Singer,et al.  Temporal binding and the neural correlates of sensory awareness , 2001, Trends in Cognitive Sciences.

[12]  Reza Ahmadi,et al.  Experimental Realization of a Reconfigurable Three Input, One Output Logic Function Based on a Chaotic Circuit , 2010, Int. J. Bifurc. Chaos.

[13]  Behnam Kia,et al.  Unstable periodic orbits and noise in chaos computing. , 2011, Chaos.

[14]  William L. Ditto,et al.  Implementation of nor Gate by a Chaotic Chua's Circuit , 2003, Int. J. Bifurc. Chaos.

[15]  Maurizio Corbetta,et al.  The human brain is intrinsically organized into dynamic, anticorrelated functional networks. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[16]  I. Campos-Cant A SIMPLE CIRCUIT WITH DYNAMIC LOGIC ARCHITECTURE OF BASIC LOGIC GATES , 2010 .

[17]  William L. Ditto,et al.  Logic from nonlinear dynamical evolution , 2009 .

[18]  M. Jahed-Motlagh,et al.  Reconfigurable logic blocks based on a chaotic Chua circuit , 2009 .

[19]  W. Ditto,et al.  Noise tolerant spatiotemporal chaos computing. , 2014, Chaos.

[20]  Alessio Gizzi,et al.  On the coherent behavior of pancreatic beta cell clusters , 2014, 1407.7741.

[21]  Haipeng Peng,et al.  A Reconfigurable Logic Cell Based on a Simple Dynamical System , 2013 .

[22]  Walter Dandy,et al.  The Brain , 1966 .

[23]  Behnam Kia,et al.  Coupling Reduces Noise: Applying Dynamical Coupling to Reduce Local White Additive Noise , 2014, Int. J. Bifurc. Chaos.

[24]  William L. Ditto,et al.  Chaos computing: implementation of fundamental logical gates by chaotic elements , 2002 .

[25]  Behnam Kia,et al.  Synthetic Computation: Chaos Computing, Logical Stochastic Resonance, and Adaptive Computing , 2014 .

[26]  Olaf Sporns,et al.  The Non-Random Brain: Efficiency, Economy, and Complex Dynamics , 2010, Front. Comput. Neurosci..

[27]  J. Rinzel,et al.  Model for synchronization of pancreatic beta-cells by gap junction coupling. , 1991, Biophysical journal.

[28]  A. Chun On the brain , 2007 .

[29]  D. Plenz,et al.  The organizing principles of neuronal avalanches: cell assemblies in the cortex? , 2007, Trends in Neurosciences.

[30]  Georgi S. Medvedev,et al.  Shaping bursting by electrical coupling and noise , 2011, Biological Cybernetics.

[31]  Eugene M. Izhikevich,et al.  Simple model of spiking neurons , 2003, IEEE Trans. Neural Networks.

[32]  Yong-Bin Kim,et al.  CNTFET-Based Design of Ternary Logic Gates and Arithmetic Circuits , 2011, IEEE Transactions on Nanotechnology.

[33]  Andreas K. Engel,et al.  Temporal binding and the neural correlates of consciousness , 2003 .

[34]  Sudeshna Sinha,et al.  Flexible parallel implementation of logic gates using chaotic elements. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Lixiang Li,et al.  Harnessing piecewise-linear systems to construct dynamic logic architecture. , 2008, Chaos.

[36]  Behnam Kia,et al.  Chaos computing in terms of periodic orbits. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  William L. Ditto,et al.  Construction of a reconfigurable dynamic logic cell , 2005 .

[38]  Nicolas Tabareau,et al.  How Synchronization Protects from Noise , 2007, 0801.0011.

[39]  Erik M. Bollt,et al.  Review of Chaos Communication by Feedback Control of Symbolic Dynamics , 2003, Int. J. Bifurc. Chaos.

[40]  N. Barbaro,et al.  Spatiotemporal Dynamics of Word Processing in the Human Brain , 2007, Front. Neurosci..

[41]  John A. Chandy,et al.  Design of Ternary Logic Combinational Circuits Based on Quantum Dot Gate FETs , 2013, IEEE Transactions on Very Large Scale Integration (VLSI) Systems.

[42]  Keivan Navi,et al.  A universal method for designing low-power carbon nanotube FET-based multiple-valued logic circuits , 2013, IET Comput. Digit. Tech..

[43]  T. Womelsdorf,et al.  The role of neuronal synchronization in selective attention , 2007, Current Opinion in Neurobiology.

[44]  H. Meissner Electrophysiological evidence for coupling between β cells of pancreatic islets , 1976, Nature.

[45]  William L. Ditto,et al.  DYNAMICS BASED COMPUTATION , 1998 .

[46]  E. Rojas,et al.  Electrical coupling between cells in islets of langerhans from mouse , 2005, The Journal of Membrane Biology.