Manuscript Topics

Many dynamical systems, as examples from small-scale neuronal systems and genomic systems in humans to large-scale ecosystems of earth that impact climate change, are featured by nonlinear and complex patterns in spatial and temporal dimensions. These phenomena carry significant information and regulate downstream dynamics. Understanding the mechanisms underlying such events by quantitative modeling represents a mathematical challenge of current interest. Yet all these systems share similar dynamical system issues in ordinary/partial differential equations such as bifurcation, stability, oscillations, and stochastic noise, as well as issues in determining hidden model parameters from experimental data sets and computational errors of the models.

The special issue may include but is not restricted to:
(a) Dynamics and computation of neuronal systems
• Modeling and dynamical analysis of biological neurons and neuronal networks.
• Generation, encoding, and transduction of neuronal signals and patterns.
• Modeling and analysis of cognitive information processing mechanisms
• Dynamic abnormality in neuronal systems due to diseases.
(b) Dynamics of immune systems
• Modeling biomedical processes, including tumor growth, cardio-vascular diseases, infection, and healing, mediated by immunologic mechanisms.
• Analysis of mathematical models for dynamics features such as instabilities and bifurcations.
• Modeling wound healing and inflammatory responses, including cell-to-cell interactions, foreign body reactions, and quantitative and qualitative comparison with experimental data.
(c) Bifurcations and dynamics phenomenon in mathematical physics, such as nonlinear optics, photonics etc.

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