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Numerous studies, and in particular the works of Freeman and others, have shown the possible relevance of chaos to various functions of the brain. The verification of these claims has mostly been experimental in nature, since a formal mathematical analysis is often intractable because of the sheer magnitude of the number (billions) of neurons in the brain. Consequently, a formal analysis of such models has only been achieved for 'small-scale systems' of neural networks (NNs). As opposed to this, the aim of this paper is to understand how we can model the brain as a so-called 'large-scale system' for analyzing various neurological conditions such as epilepsy, schizophrenia, etc. In particular, we explore a large-scale NN model suitable for the piriform cortex which is acclaimed for its chaotic behavior from clinical experiments. In addition, the piriform cortex is easy to model because it appears to be 'almost independent' of other portions of the brain. To achieve this, we describe its behavior by moving the analysis from the time space into the phase space of the electroencephalogram (EEG) signals. Although the model of the piriform cortex contains hundreds of variables, we utilize the concept that useful information can be extracted from a single EEG signal which, in turn, can be perceived as a time series computed from the artificial electrodes. Indeed, this transformation, i.e. from the time space of a time series to its corresponding phase space, is considered mandatory to extract the nonlinear characteristics related with chaos. By studying the piriform cortex model in this manner, we demonstrate that we can generate certain desirable phenomena by modifying some of the underlying control parameters. More specifically, we investigate the problem of density and strength, the problem of connectivity and the problem of stimulus frequency, and show their relevance to neurological conditions such as epilepsy and schizophrenia.