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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/14.04%3A_Linear_Stability_Analysis_of_Reaction-Diffusion_SystemsYou may have found that the linear stability analysis of continuous field models isn’t as easy as that of non-spatial models. For the latter, we have a very convenient tool called the Jacobian matrices...You may have found that the linear stability analysis of continuous field models isn’t as easy as that of non-spatial models. For the latter, we have a very convenient tool called the Jacobian matrices, and the stability analysis is just calculating a Jacobian matrix and then investigating its eigenvalues. Everything is so mechanistic and automatic, compared to what we went through in the previous section. You may wonder, aren’t there any easier shortcuts in analyzing the stability of continuous
- https://math.libretexts.org/Bookshelves/Scientific_Computing_Simulations_and_Modeling/Introduction_to_the_Modeling_and_Analysis_of_Complex_Systems_(Sayama)/18%3A_Dynamical_Networks_III__Analysis_of_Network_Dynamics/18.04%3A_Mean-Field_Approximation_of_Discrete-State_NetworksAnalyzing the dynamics of discrete-state network models requires a different approach, because the assumption of smooth, continuous state space, on which the linear stability analysis is based on, no ...Analyzing the dynamics of discrete-state network models requires a different approach, because the assumption of smooth, continuous state space, on which the linear stability analysis is based on, no longer applies. This difference is similar to the difference between continuous field models and cellular automata (CA).
- https://math.libretexts.org/Bookshelves/Scientific_Computing_Simulations_and_Modeling/Introduction_to_the_Modeling_and_Analysis_of_Complex_Systems_(Sayama)/15%3A_Basics_of_Networks/15.01%3A_Network_ModelsWe are now moving into one of the most recent developments of complex systems science: networks.
- https://math.libretexts.org/Bookshelves/Scientific_Computing_Simulations_and_Modeling/Introduction_to_the_Modeling_and_Analysis_of_Complex_Systems_(Sayama)/01%3A_Introduction_to_Modeling_and_Analysis
- https://math.libretexts.org/Bookshelves/Scientific_Computing_Simulations_and_Modeling/Introduction_to_the_Modeling_and_Analysis_of_Complex_Systems_(Sayama)/03%3A_Basics_of_Dynamical_SystemsA dynamical system is a system whose state is uniquely specified by a set of variables and whose behavior is described by predefined rules.
- https://math.libretexts.org/Bookshelves/Scientific_Computing_Simulations_and_Modeling/Introduction_to_the_Modeling_and_Analysis_of_Complex_Systems_(Sayama)/02%3A_Fundamentals_of_Modeling
- 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)/05%3A_DiscreteTime_Models_II__Analysis
- https://math.libretexts.org/Bookshelves/Scientific_Computing_Simulations_and_Modeling/Introduction_to_the_Modeling_and_Analysis_of_Complex_Systems_(Sayama)/16%3A_Dynamical_Networks_I__Modeling/16.03%3A_Simulating_Dynamics_of_NetworksDynamics of networks models capture completely different kinds of network dynamics, i.e., changes in network topologies. This includes the addition and removal of nodes and edges over time. As discuss...Dynamics of networks models capture completely different kinds of network dynamics, i.e., changes in network topologies. This includes the addition and removal of nodes and edges over time. As discussed in the previous chapter, such dynamic changes of the system’s topology itself are quite unusual from a traditional dynamical systems viewpoint, because they would make it impossible to assume a well-defined static phase space of the system.
- https://math.libretexts.org/Bookshelves/Scientific_Computing_Simulations_and_Modeling/Introduction_to_the_Modeling_and_Analysis_of_Complex_Systems_(Sayama)/18%3A_Dynamical_Networks_III__Analysis_of_Network_Dynamics/18.01%3A_Dynamics_of_Continuous-State_NetworksWe will now switch gears to the analysis of dynamical properties of networks. We will first discuss how some of the analytical techniques we already covered in earlier chapters can be applied to dynami...We will now switch gears to the analysis of dynamical properties of networks. We will first discuss how some of the analytical techniques we already covered in earlier chapters can be applied to dynamical network models, and then we will move onto some additional topics that are specific to networks.
- https://math.libretexts.org/Bookshelves/Scientific_Computing_Simulations_and_Modeling/Introduction_to_the_Modeling_and_Analysis_of_Complex_Systems_(Sayama)/04%3A_DiscreteTime_Models_I__Modeling/406%3A_Building_Your_Own_Model_Equations_with_Multiple_VariablesWe can take one more step to increase the complexity of the model building, by including more than one variable. Following the theme of population growth, let’s consider ecological interactions betwee...We can take one more step to increase the complexity of the model building, by including more than one variable. Following the theme of population growth, let’s consider ecological interactions between two species.
