Differential Evolution approach and parameter estimation of chaotic

Parameter estimation still remains a challenge in many important applications. There is a need to develop methods that utilize achievements in modern computational systems with growing capabilities. Owing to this fact different kinds of Evolutionary Algorithms are becoming an especially perspective field of research. The main aim of this thesis is to explore theoretical aspects of a specific type of Evolutionary Algorithms class, the Differential Evolution (DE) method, and implement this algorithm as codes capable to solve a large range of problems. Matlab, a numerical computing environment provided by MathWorks inc., has been utilized for this purpose. Our implementation empirically demonstrates the benefits of a stochastic optimizers with respect to deterministic optimizers in case of stochastic and chaotic problems. Furthermore, the advanced features of Differential Evolution are discussed as well as taken into account in the Matlab realization. Test "toycase" examples are presented in order to show advantages and disadvantages caused by additional aspects involved in extensions of the basic algorithm. Another aim of this paper is to apply the DE approach to the parameter estimation problem of the system exhibiting chaotic behavior, where the well-known Lorenz system with specific set of parameter values is taken as an example. Finally, the DE approach for estimation of chaotic dynamics is compared to the Ensemble prediction and parameter estimation system (EPPES) approach which was recently proposed as a possible solution for similar problems.

Adaptive Dynamics of Resource Specialization

Ecological specialization in resource utilization has various facades ranging from nutritional resources via host use of parasites or phytophagous insects to local adaptation in different habitats. Therefore, the evolution of specialization affects the evolution of most other traits, which makes it one of the core issues in the theory of evolution. Hence, the evolution of specialization has gained enormous amounts of research interest, starting already from Darwin’s Origin of species in 1859. Vast majority of the theoretical studies has, however, focused on the mathematically most simple case with well-mixed populations and equilibrium dynamics. This thesis explores the possibilities to extend the evolutionary analysis of resource usage to spatially heterogeneous metapopulation models and to models with non-equilibrium dynamics. These extensions are enabled by the recent advances in the field of adaptive dynamics, which allows for a mechanistic derivation of the invasion-fitness function based on the ecological dynamics. In the evolutionary analyses, special focus is set to the case with two substitutable renewable resources. In this case, the most striking questions are, whether a generalist species is able to coexist with the two specialist species, and can such trimorphic coexistence be attained through natural selection starting from a monomorphic population. This is shown possible both due to spatial heterogeneity and due to non-equilibrium dynamics. In addition, it is shown that chaotic dynamics may sometimes inflict evolutionary suicide or cyclic evolutionary dynamics. Moreover, the relations between various ecological parameters and evolutionary dynamics are investigated. Especially, the relation between specialization and dispersal propensity turns out to be counter-intuitively non-monotonous. This observation served as inspiration to the analysis of joint evolution of dispersal and specialization, which may provide the most natural explanation to the observed coexistence of specialist and generalist species.

Parameter estimation for Chaotic or Stochastic Dynamics

Since its discovery, chaos has been a very interesting and challenging topic of research. Many great minds spent their entire lives trying to give some rules to it. Nowadays, thanks to the research of last century and the advent of computers, it is possible to predict chaotic phenomena of nature for a certain limited amount of time. The aim of this study is to present a recently discovered method for the parameter estimation of the chaotic dynamical system models via the correlation integral likelihood, and give some hints for a more optimized use of it, together with a possible application to the industry. The main part of our study concerned two chaotic attractors whose general behaviour is diff erent, in order to capture eventual di fferences in the results. In the various simulations that we performed, the initial conditions have been changed in a quite exhaustive way. The results obtained show that, under certain conditions, this method works very well in all the case. In particular, it came out that the most important aspect is to be very careful while creating the training set and the empirical likelihood, since a lack of information in this part of the procedure leads to low quality results.