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\begin{document} 

	\begin{titlepage} %titulná strana
		\centering
		\bf\large COMENIUS UNIVERSITY IN BRATISLAVA\\
		\bf\large FACULTY OF MATHEMATICS, PHYSICS AND INFORMATICS
		\vspace{220pt}\\
		\bf\large Title of the Thesis\\
		\rm\large Bachelor thesis\\
		\flushleft\rm\normalsize	
		\vspace{160pt}
		\rm Study program: Managerial Mathematics\\
		Field of Study: Mathematics\\
		Department: Department of Mathematical Analysis and Numerical Mathematics
\\
		Supervisor: SUPERVISOR WITH TITLES
\\
		\vspace*{\fill}
		\bf Bratislava 2023\\
		\bf Your Name	
	\end{titlepage}

	\includepdf[pages={1}]{1572695882032.PDF}
	\includepdf[pages={1}]{1572695847030.PDF}

	\begin{titlepage} %čestné prehlásenie
		\vspace*{\fill}
		{\setlength{\parindent}{0cm} Hereby I declare that I have done this piece of work alone, with an aid of my supervisor\dots } \\
		\flushright	........................................\\
		Your Name	
	\end{titlepage}

	\section*{Acknowledgements}	
	\addcontentsline{toc}{section}{\protect\numberline{}Acknowledgements}
	Some warm words here, to be filled in later on.
	\newline

	\noindent 
	%2. some warm words here as well
	\newpage
	
	\section*{Abstract}
	\addcontentsline{toc}{section}{\protect\numberline{}Abstract}
	aaaaaaaaaaa\_EN  
	\vspace{20pt}\\
	\bf Keywords: \rm \dots
		
	\newpage
	
	\section*{Abstrakt}
	\addcontentsline{toc}{section}{\protect\numberline{}Abstrakt}
	aaaaaaaaaaa\_SK    
	\vspace{20pt}\\
	\bf Kľúčové slová: \rm \dots
		
	\newpage
	
	\tableofcontents
	\newpage
	
	\chapter*{Introduction}
	\addcontentsline{toc}{section}{\protect\numberline{}Introduction}
	Introduction text in here...  
	\newpage
	
	\chapter{FitzHugh-Nagumo (FHN) Model}
		\section{Subsection 1.1}	
			
		\section{Subsection 1.2}
			\subsection{Subsection 1.2.1} 

		
			

						
	\chapter{Basic Mathematical Terms and Assertions}
		\label{HA}

		\section{Existence and Uniqueness of Solution of the Cauchy Problem for first order differential equation}
		
		
		We will be interested in solutions of the following Cauchy problem \cite{Demetrian_skripta}
		
		\begin{equation}
			\begin{array}{l}
			\dot{x}(t) = F(t,x), \\
			x(t_{0})=x_{0}
			\end{array} 
		\end{equation}	

		

		
		\subsection{Peano Theorem}
		
		Let $\mathcal{M}\subset\mathbb{R}^{2}$ is an open set. Let the function
		
		\begin{equation}
		F: \mathcal{M} \to \mathbb{R} 
		\end{equation}	
		

		
		
		\subsection{Picard Theorem}	
		Let the function
		
		\begin{equation}
		F: \mathbb{R}^{2} \to \mathbb{R},(t,x) \mapsto F(t,x) \nonumber 
		\end{equation}
		be Lipschitz in second variable with Lipschitz constant $L$ on rectangle


		   
		 \begin{figure}[!h]
		 	\centering
		 	\includegraphics[width=0.8\textwidth]{pics/FHN_19.png}
			\caption{Solution of Eq.(\ref{Example_bounded_1}) for $\alpha=2,x_0=2,x_{max}=100$} 
		 	\label{FHN_19.png}
		 \end{figure}
	
	
		
		

		
	\chapter{Dynamics of FHN Model}
	
		\section{FHN model with general parameters}
		
		The FitzHugh-Nagumo model is described by system of differential equations \cite{Izhikevich} 
		
		\begin{equation}
		\label{FHN_general}
		\begin{array}{l}
		\dot{v}=v(a-v)(v-1)-w+I_{ext}  \\
		\dot{w}=bv-cw 
		\end{array} 
		\end{equation}
		
	
	\chapter*{Conclusions}
	\addcontentsline{toc}{section}{\protect\numberline{}Conclusions}
	Some conclusion text in here...
	
	\newpage
	\bibliographystyle{unsrt}	
	\bibliography{References}

	
\end{document}		