Mathematical derivations revealed a chaotic, memristor-based circuit in which different oscillating phases can coexist along six different lines.
Chaotic circuits, unlike ordinary electronic circuits, can generate oscillating electrical signals that never repeat over time while displaying underlying mathematical patterns. Previous research has designed systems in which multiple oscillating phases can coexist along mathematically defined “lines of equilibrium” to broaden the potential applications of these circuits. A team led by JanarthananRamadoss at the Chennai Institute of Technology, India, designed a chaotic circuit with six distinct lines of equilibrium in new research published in The European Physical Journal Special Topics.
Chaotic systems are now widely studied in many fields, ranging from biology and chemistry to engineering and economics. If the team’s circuit is experimentally realised, it could provide researchers with unprecedented opportunities to study these systems. In practise, their design could be used for robotic motion control, secure password generation, and new developments in the Internet of Things—networks of everyday objects that can gather and share data.
Memristors are the building blocks of chaotic circuits: electrical components that limit the amount of current flowing through the circuit while remembering the amount of charge that has previously flowed through them. Recently, there has been a lot of interest in chaotic memristor circuits with multiple lines of equilibrium. These lines define the boundaries between different oscillation phases, allowing multiple phases to coexist along them. So far, systems with up to five equilibrium lines have been proposed.
Ramadoss’ team discovered a system with six of these lines through new derivations. The researchers observed a variety of complex dynamics by changing the parameters and starting conditions of their system, including the division of oscillating bubbles and the coexistence of objects that would normally be attracted to each other and merge into a single object. To test the viability of their ideas, the team has created a memristor-based circuit, which they hope to demonstrate in future experiments.