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  • https://math.libretexts.org/Bookshelves/Scientific_Computing_Simulations_and_Modeling/Introduction_to_the_Modeling_and_Analysis_of_Complex_Systems_(Sayama)/14%3A_Continuous_Field_Models_II__Analysis
  • https://math.libretexts.org/Bookshelves/Scientific_Computing_Simulations_and_Modeling/Introduction_to_the_Modeling_and_Analysis_of_Complex_Systems_(Sayama)/14%3A_Continuous_Field_Models_II__Analysis/14.03%3A_Linear_Stability_Analysis_of_Continuous_Field_Models
    We can apply the linear stability analysis to continuous field models. This allows us to analytically obtain the conditions for which a homogeneous equilibrium state of a spatial system loses its stabi...We can apply the linear stability analysis to continuous field models. This allows us to analytically obtain the conditions for which a homogeneous equilibrium state of a spatial system loses its stability and thereby the system spontaneously forms non-homogeneous spatial patterns. Note again that the homogeneous equilibrium state discussed here is no longer a single point, but it is a straight line (or a flat plane) that covers the entire spatial domain.
  • https://math.libretexts.org/Bookshelves/Scientific_Computing_Simulations_and_Modeling/Introduction_to_the_Modeling_and_Analysis_of_Complex_Systems_(Sayama)/13%3A_Continuous_Field_Models_I__Modeling/13.01%3A_Continuous_Field_Models_with_Partial_Differential_Equations
    Spatio-temporal dynamics of complex systems can also be modeled and analyzed using partial differential equations (PDEs), i.e., differential equations whose independent variables include not just time...Spatio-temporal dynamics of complex systems can also be modeled and analyzed using partial differential equations (PDEs), i.e., differential equations whose independent variables include not just time, but also space.

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