Chaotic dynamics in a class of generalized memristive maps

Area of Science:

• Nonlinear Dynamics
• Chaos Theory
• Solid-State Physics

Background:

• Memristors exhibit memory effects influencing nonlinear system dynamics.
• Generalized Ohm's law describes nonlinear voltage-current relationships, unlike classical linear Ohm's law.
• Memristive systems offer potential for complex dynamical behaviors and novel applications.

Purpose of the Study:

• To introduce and investigate a discrete memristive system model using a generalized Ohm's law.
• To explore the complex dynamical behaviors, including chaos and hyperchaos, within this model.
• To experimentally validate the model's predictions using a hardware implementation.

Main Methods:

• Modeling discrete memristive systems with a generalized Ohm's law (cubic function).
• Analyzing dynamical behavior using Lyapunov exponents to identify chaos and hyperchaos.
• Implementing the memristive maps on a hardware device for experimental signal acquisition.

Main Results:

• Demonstrated the existence of attractors with one or two positive Lyapunov exponents, indicating chaotic and hyperchaotic dynamics.
• Observed the coexistence of infinitely many attractors, highlighting the system's rich dynamical complexity.
• Acquired analog voltage signals experimentally, confirming the hardware implementation of the memristive maps.

Conclusions:

• The discrete memristive system model with generalized Ohm's law exhibits rich and complex dynamics, including chaos and hyperchaos.
• The study confirms the potential for memristors in generating complex dynamics, with implications for future applications.
• Experimental validation supports the theoretical findings and the practical implementation of memristive systems.