Belousov-Zhabotinsky "Chemical Neuron" as a Binary and Fuzzy Logic Processor

We demonstrate experimentally that the well-known oscillatory BelousovZhabotinsky (BZ) reaction can be exploited to process both Boolean and fuzzy logic if the input variables are either the volumes or the phase of addition of pulse-injected solutions of inhibitor (bromide) and activator (silver ion) and the output variable is the oscillation period. Analysis of the relations between the input and the output variables reveals that this oscillating chemical reaction is suitable to process infinite-valued fuzzy logic, and that all fundamental fuzzy logic operators (AND, OR, NOT) can be implemented with it. We discuss the possibility for biological oscillators such as neurons or pacemaker cells to process information using principles of fuzzy logic.

[1]  J. Mendel.  Fuzzy logic systems for engineering: a tutorial , 1995, Proc. IEEE.

[2]  Ebrahim Mamdani,et al.  Applications of fuzzy algorithms for control of a simple dynamic plant , 1974 .

[3]  Lotfi A. Zadeh,et al.  Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic , 1997, Fuzzy Sets Syst..

[4]  J. Ross,et al.  Computational functions in biochemical reaction networks. , 1994, Biophysical journal.

[5]  Eugene M. Izhikevich,et al.  Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting , 2006 .

[6]  Pier Luigi Gentili,et al.  The fundamental Fuzzy logic operators and some complex boolean logic circuits implemented by the chromogenism of a spirooxazine. , 2011, Physical chemistry chemical physics : PCCP.

[7]  Pier Luigi Gentili,et al.  Molecular Fuzzy Inference Engines - Development of Chemical Systems to Process Fuzzy Logic at the Molecular Level , 2011, ICAART.

[8]  Pier Luigi Gentili,et al.  Boolean and fuzzy logic gates based on the interaction of flindersine with bovine serum albumin and tryptophan. , 2008, The journal of physical chemistry. A.

[9]  F. Hynne,et al.  Oscillations of bromous acid, hypobromous acid, bromide, and cerium(4+) concentrations in the Belousov-Zhabotinskii reaction reconstructed from quenching experiments , 1991 .

[10]  Andrew Adamatzky.  Topics in Reaction-Diffusion Computers , 2011 .

[11]  Ebrahim H. Mamdani,et al.  An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller , 1999, Int. J. Hum. Comput. Stud..

[12]  I. Epstein,et al.  An Introduction to Nonlinear Chemical Dynamics , 1998 .

[13]  P. Warren.  The future of computing - new architectures and new technologies. 2. Parallelism and information , 2002 .

[14]  Kenneth Showalter,et al.  Logic gates in excitable media , 1995 .

[15]  K. Szaciłowski.  Digital information processing in molecular systems. , 2008, Chemical reviews.

[16]  Peter Ruoff,et al.  How bromate oscillators are controlled , 1988 .

[17]  Peter Ruoff,et al.  Phase response relationships of the closed bromide-perturbed Belousov-Zhabotinsky reaction. Evidence of bromide control of the free oscillating state without use of a bromide-detecting device , 1984 .

[18]  M. Sugeno,et al.  A review and comparison of six reasoning methods , 1993 .

[19]  C. Gammons,et al.  The stability of aqueous silver bromide and iodide complexes at 25–300°C: Experiments, theory and geologic applications , 1997 .

[20]  D. Bray.  Protein molecules as computational elements in living cells , 1995, Nature.

[21]  Pier Luigi Gentili,et al.  Molecular processors: from qubits to fuzzy logic. , 2011, Chemphyschem : a European journal of chemical physics and physical chemistry.

[22]  A. Winfree.  Phase control of neural pacemakers. , 1977, Science.

[23]  Konrad Szaciłowski,et al.  Digital Information Processing in Molecular Systems , 2008 .

[24]  Pier Luigi Gentili,et al.  Boolean and fuzzy logic implemented at the molecular level , 2007 .

[25]  Kenneth Showalter,et al.  Chemical Wave Logic Gates , 1996 .

[26]  Lotfi A. Zadeh,et al.  Fuzzy Logic , 2009, Encyclopedia of Complexity and Systems Science.

[27]  Michio Sugeno,et al.  A fuzzy-logic-based approach to qualitative modeling , 1993, IEEE Trans. Fuzzy Syst..

[28]  Lotfi A. Zadeh.  Toward Human Level Machine Intelligence - Is It Achievable? The Need for a Paradigm Shift , 2008 .

[29]  Jerzy Gorecki,et al.  Basic Information Processing Operations with Pulses of Excitation in a Reaction-Diffusion System , 2009, Int. J. Unconv. Comput..

[30]  Pier Luigi Gentili,et al.  Pulse-coupled chemical oscillators with time delay. , 2012, Angewandte Chemie.

[31]  L. I. Kheifets.  Periodic liquid-phase reactions with gas liberation on porous catalysts , 1985 .

[32]  W. Snodgrass.  Physiology , 1897, Nature.

[33]  Jan Szymanski,et al.  Chemical Pulses Propagating Inside a Narrowing Channel and Their Possible Computational Applications , 2010, Int. J. Unconv. Comput..

[34]  Andrew Adamatzky,et al.  Towards Arithmetic Circuits in Sub‐Excitable Chemical Media , 2011 .