Hyperchaos and multistability in the model of two interacting microbubble contrast agents

Area of Science:

• Nonlinear Dynamics
• Acoustics
• Biophysics

Background:

• Microbubbles encapsulated in viscoelastic shells are crucial contrast agents for ultrasound imaging.
• These microbubbles also hold potential for targeted drug delivery and noninvasive therapies.
• Understanding their dynamic behavior is essential for optimizing these applications.

Purpose of the Study:

• To investigate the nonlinear dynamics of two coupled microbubbles interacting via the Bjerknes force under an external ultrasound field.
• To identify and characterize different types of complex oscillations, including chaotic and hyperchaotic regimes.
• To explore the bifurcation pathways leading to these complex dynamics and the phenomenon of multistability.

Main Methods:

• Modeling a five-dimensional nonlinear dynamical system for two interacting microbubbles.
• Analyzing bifurcation scenarios, including Feigenbaum cascade and torus destruction, for chaotic dynamics.
• Proposing a novel bifurcation scenario for hyperchaotic dynamics involving homoclinic chaotic attractors.

Main Results:

• Observed periodic, quasiperiodic, chaotic, and hyperchaotic oscillations in the microbubble system.
• Identified distinct bifurcation routes to chaos and hyperchaos.
• Demonstrated significant multistability, with various coexisting attractors, including hyperchaotic regimes.

Conclusions:

• The model of two coupled microbubbles presents a physically relevant system exhibiting complex nonlinear dynamics.
• The study reveals new insights into bifurcation mechanisms for chaos and hyperchaos.
• The observed multistability, particularly involving hyperchaos, offers new avenues for advanced applications in ultrasound-based technologies.