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The Impact of Nonlocal Coupling on Wavefront Propagation in Bistable Oscillator Ensembles: A Numerical Study


Core Concepts
Nonlocal coupling can be used to control the speed and resilience of wavefront propagation in ensembles of bistable oscillators, even under the influence of noise.
Abstract
  • Bibliographic Information: Semenov, V.V. (2024). The impact of nonlocal coupling on deterministic and stochastic wavefront propagation in an ensemble of bistable oscillators. Physics Letters A. Preprint submitted to Physics Letters A.

  • Research Objective: This study investigates the influence of nonlocal coupling on wavefront propagation in a system of coupled bistable oscillators, considering both deterministic and stochastic scenarios.

  • Methodology: The research employs numerical simulations of an ensemble of locally coupled overdamped bistable oscillators. The impact of coupling strength, coupling radius, and noise (multiplicative and additive) on wavefront propagation speed and pattern formation is systematically analyzed.

  • Key Findings:

    • Increasing the coupling radius, while keeping the coupling strength constant, accelerates wavefront propagation in both deterministic and stochastic settings.
    • Nonlocal coupling can mitigate the destructive effects of noise on propagating wavefronts, preserving patterns that would be disrupted under local coupling.
    • Additive noise, typically disregarded in wavefront control, can accelerate wavefront propagation in asymmetric systems.
  • Main Conclusions: Nonlocal coupling offers a robust mechanism for controlling wavefront propagation in bistable oscillator ensembles. It allows for fine-tuning propagation speed and enhances resilience against noise, highlighting its potential in various physical and biological systems.

  • Significance: This research contributes to the understanding of nonlocal coupling effects in complex systems, extending the existing knowledge of wavefront control mechanisms.

  • Limitations and Future Research: The study focuses on a simplified model of bistable oscillators. Exploring the impact of nonlocal coupling on wavefront dynamics in more realistic models with complex local dynamics could provide further insights. Investigating the interplay of additive and multiplicative noise in the context of nonlocal coupling is another promising avenue for future research.

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Stats
The total number of oscillators used in the simulations is N = 103. The time step used for numerical integration is ∆t = 0.001. The total integration time for simulations is t_total = 10^4. The mean wavefront propagation velocity was calculated as an average of 40 simulations. Additive noise-induced destruction of propagating fronts was observed at D_critical ≈ 0.064.
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Deeper Inquiries

How might the findings of this study be applied to control wavefront propagation in real-world systems, such as biological tissues or chemical reactions?

This study highlights the significant role of nonlocal coupling in controlling both deterministic and stochastic wavefront propagation. This understanding can be applied to manipulate wave-like phenomena in various real-world systems: 1. Biological Tissues: Cardiac Tissue: Cardiac arrhythmias often involve undesirable spiral waves of electrical excitation. By manipulating the coupling between cardiac cells, potentially through targeted drug delivery or optogenetic techniques, it might be possible to disrupt these arrhythmic wavefronts and restore normal heart rhythm. Neural Tissue: Information processing in the brain involves complex spatiotemporal patterns of neural activity. Understanding how nonlocal coupling influences wave propagation in neural networks could lead to new strategies for treating neurological disorders or enhancing cognitive function. Wound Healing: Wound healing involves the coordinated movement and proliferation of cells. By manipulating cell-cell interactions, it might be possible to accelerate the propagation of healthy cells into the wounded area, promoting faster healing. 2. Chemical Reactions: Controlling Reaction Rates: In chemical reactions exhibiting bistability, nonlocal coupling could be used to control the speed and direction of reaction fronts. This could be achieved by introducing catalysts or inhibitors that influence long-range interactions between reacting molecules. Pattern Formation: Nonlocal coupling can lead to the emergence of complex spatial patterns in chemical reactions, as seen in the Belousov-Zhabotinsky reaction. By manipulating the coupling parameters, it might be possible to control the size, shape, and stability of these patterns, with potential applications in materials science and nanotechnology. Challenges and Considerations: Complexity of Real-World Systems: Real-world systems are significantly more complex than the simplified model used in this study. Factors such as heterogeneity, anisotropy, and nonlinearity can significantly influence wavefront dynamics. Practical Implementation: Translating the findings of this study into practical applications will require developing techniques for precisely manipulating coupling in the target system.

Could there be scenarios where local coupling is preferable to nonlocal coupling for controlling wavefront propagation, and if so, what are the defining characteristics of such scenarios?

While the study emphasizes the benefits of nonlocal coupling, there are scenarios where local coupling might be more advantageous for controlling wavefront propagation: 1. Precise Spatial Control: Localized Activation/Inhibition: Local coupling allows for more precise spatial control over wavefront initiation and propagation. For instance, in targeted drug delivery, local release of a drug that enhances coupling between cells could be used to initiate a wavefront at a specific location. Boundary Effects: Local coupling is more sensitive to boundary conditions, which can be exploited to confine wavefronts within specific regions or guide them along desired paths. 2. Simplicity and Efficiency: Ease of Implementation: In some systems, manipulating local interactions might be easier to implement than establishing long-range nonlocal coupling. Lower Energy Requirements: Maintaining long-range interactions can be energetically costly. Local coupling might be more efficient in situations where energy conservation is crucial. Defining Characteristics of Scenarios Favoring Local Coupling: Need for precise spatial control over wavefront initiation and propagation. Importance of boundary effects in shaping wavefront dynamics. Systems where manipulating local interactions is more feasible or energy-efficient. Examples: Microfluidic Devices: Controlling fluid flow in microfluidic devices often relies on local interactions between fluid elements and channel walls. Optical Waveguides: Light propagation in optical waveguides is primarily governed by local interactions with the waveguide boundaries.

How does the concept of "information flow" relate to the propagation of wavefronts in complex systems, and how does nonlocal coupling influence this flow?

The propagation of wavefronts can be viewed as a form of information flow in complex systems. The wavefront carries information about the state of the system, and its propagation spreads this information to different parts of the system. Information Flow in Locally Coupled Systems: Local Propagation: In locally coupled systems, information flows directly from one element to its immediate neighbors. This typically results in a diffusive spread of information, analogous to heat diffusion. Speed Limited by Diffusion: The speed of information flow is limited by the strength of local coupling, analogous to the diffusion coefficient. Nonlocal Coupling's Influence on Information Flow: Long-Range Interactions: Nonlocal coupling introduces long-range interactions, allowing elements to communicate directly with others located far away. Enhanced Information Flow: This long-range communication can significantly enhance the speed and efficiency of information flow, as seen in the study's finding that increasing the coupling radius speeds up wavefront propagation. Emergent Behavior: Nonlocal coupling can lead to the emergence of complex collective behaviors, such as synchronization or pattern formation, which can be interpreted as emergent forms of information processing. Examples: Social Networks: The spread of information (e.g., news, rumors) in social networks is heavily influenced by nonlocal connections between individuals. Financial Markets: Global financial markets exhibit strong nonlocal coupling, with events in one market rapidly influencing others worldwide. In summary, nonlocal coupling plays a crucial role in shaping information flow in complex systems by enabling long-range interactions and facilitating the emergence of collective behaviors.
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