The paper is devoted to the study of mathematical model of chaotic oscillator, as well the ability of its employment in low-power wide-area network (LPWAN) communication systems. For this reason, modified Chua circuit with four state variables and nonlinear function is presented and analyzed. The impact of system’s parameters on the dynamics of the oscillator is investigated and three basic modes of operation are found. The obtained chaotic modes of the proposed dynamical system could provide possibility to build secure and robust communication system, moreover the variations of system parameters could be used for implementation of multi-user communication system. Besides that, the chaotic synchronization method, based on the drive-response system employment with linear feedback is described and its properties are studied for differing initial conditions of state variables in drive and response oscillators. The most significant results of research are presented in the conclusions part.