Anti-synchronization of a M-Hopfield neural network with generalized hyperbolic tangent activation function

This paper analyzes non-integer Hopfield neural network dynamics introducing the hyperbolic tangent transfer function generalized by the Mittag-Leffler function and the M-truncated derivative with constant and variable order. The novel neural network’s (ANN) behaviors are studied through their dynam...

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Bibliographic Details
Published in:The European physical journal. ST, Special topics Vol. 231; no. 10; pp. 1801 - 1814
Main Authors: Viera-Martin, E., Gómez-Aguilar, J. F., Solís-Pérez, J. E., Hernández-Pérez, J. A., Olivares-Peregrino, V. H.
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.08.2022
Springer Nature B.V
Subjects:
Atomic
Chaos theory
Chaotic Variable-Order Fractional Neural Networks
Classical and Continuum Physics
Condensed Matter Physics
Decay rate
Dynamics
Hyperbolic functions
Integers
Materials Science
Measurement Science and Instrumentation
Molecular
Neural networks
Optical and Plasma Physics
Physics
Physics and Astronomy
Random numbers
Regular Article
Synchronism
Transfer functions
ISSN:1951-6355, 1951-6401
Online Access:Get full text
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Summary:This paper analyzes non-integer Hopfield neural network dynamics introducing the hyperbolic tangent transfer function generalized by the Mittag-Leffler function and the M-truncated derivative with constant and variable order. The novel neural network’s (ANN) behaviors are studied through their dynamics depicted in phase portraits and the 0-1 test to determine where the ANN displays strong chaotic behaviors. According to the numerical results, the generalized Hopfield (M-HNTF) reveals weak chaotic dynamics with constant values under 0.99 and regular behaviors lower than 0.8. Considering the variable order, the chaotic behaviors depend on the decay rate of the time-varying function. Due to this, we got systems with weak chaotic dynamics until strong chaotic dynamics. Next, we used two scenarios to anti-synchronize a system master and a slave system. The first considering a dynamic, chaotic system and a regular system, the second: two M-HNTF with variable order. Numerical results illustrate those mentioned above, showing the control aim. Getting new chaotic dynamics from non-integer systems with variable order is essential to develop protocols to offer secure communications, new random number generators, image encrypts schemes, to name a few.
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ISSN:1951-6355
1951-6401
DOI:10.1140/epjs/s11734-022-00456-2