Multi-valued static memory with resonant tunneling diodes as natural source of chaos

Multi-valued static memory with resonant tunneling diodes as natural source of chaos

WoS Article

This paper brings deep study focused on dynamical behavior associated with a multi-valued static memory (MVSM) cell composed by a pair of the resonant tunneling diodes. Ampere–voltage characteristic of these diodes is approximated by the piecewise-linear scalar function with two positive breakpoints. Initial linear analysis supposes separation of a state space into nine affine segments, while local vector field geometry and dynamical flow in each region are graphically visualized. It is shown that discovered chaotic solution is not a numerical artifact, is robust and can generate various dense structurally stable strange attractors. For numerical investigations concepts of the largest Lyapunov exponent, the basins of attraction and a conventional signal analysis are adopted. MVSM dynamics is then implemented as the lumped electronic circuits using different but universal analog design approaches. Proposed oscillators are optimized with respect to the simple one-to-one relations between the mathematical model parameters and adjustable-by-hand circuit components. The constructed chaotic oscillators strictly utilize only commercially available active devices. This makes true experimental verification of idea that chaos exists inside narrow regions of a hyperspace of the internal MVSM system parameters possible and easy task.

This paper brings deep study focused on dynamical behavior associated with a multi-valued static memory (MVSM) cell composed by a pair of the resonant tunneling diodes. Ampere–voltage characteristic of these diodes is approximated by the piecewise-linear scalar function with two positive breakpoints. Initial linear analysis supposes separation of a state space into nine affine segments, while local vector field geometry and dynamical flow in each region are graphically visualized. It is shown that discovered chaotic solution is not a numerical artifact, is robust and can generate various dense structurally stable strange attractors. For numerical investigations concepts of the largest Lyapunov exponent, the basins of attraction and a conventional signal analysis are adopted. MVSM dynamics is then implemented as the lumped electronic circuits using different but universal analog design approaches. Proposed oscillators are optimized with respect to the simple one-to-one relations between the mathematical model parameters and adjustable-by-hand circuit components. The constructed chaotic oscillators strictly utilize only commercially available active devices. This makes true experimental verification of idea that chaos exists inside narrow regions of a hyperspace of the internal MVSM system parameters possible and easy task.

chaos; linear topological conjugacy; multi-valued static memory; resonant tunneling diodes; strange attractor

chaos; linear topological conjugacy; multi-valued static memory; resonant tunneling diodes; strange attractor

PETRŽELA, J.

2019

05.07.2018

Springer

Netherlands

0924-090X

NONLINEAR DYNAMICS

94

3

United States of America

1867

1887

21

https://link.springer.com/article/10.1007/s11071-018-4462-0

http://hdl.handle.net/