# New Chaotic Dynamical System with a Conic-Shaped Equilibrium Located on the Plane Structure
## 1 Introduction  
It was a breakthrough discovery that the irregular motion, with a broadband frequency spectrum with Gaussian-like distribution and extreme sensitivity to changes of the initial conditions, can be observed in the class of autonomous dynamical systems with three degrees of freedom. Such behavior, now known as chaotic solution, has often been misinterpreted as a mixture of harmonic signals and noise. Research works have focused on nonlinear dynamics connected with chaos theory, proving that chaos is not a numerical artifact, but represents robust behavior and has nothing to do with stochastic processes. Since 1963, when [PERSON] first noticed and described deterministic chaos [1], numerical and experimental observations of the chaotic attractors have been reported in many scientific fields. Chaotic phenomena have been observed in reaction-diffusion systems in chemistry [2], fundamental models of classical mechanics such as pendulum with periodic excitations [3], mathematical models describing fluid dynamics [4] and hydrodynamics [5]. Unique features of chaotic signals have been registered in brain activity [6] or electrocardiogram [7] data. The emergence of a population of different species in biology [8], commodity exchange in economy [9] and time-dependent models of many ecological situations [10] are other examples of dynamical systems that are subject to chaotic dynamics. By referring to this knowledge, the presence of chaos in an evolution equation [11] and electronic circuits (both lumped and with spread parameters) seems to be obvious and logical. Besides the mentioned research, works narrowly targeting specific scientific areas, general analysis of differential equations and properties of available solutions, automatically touches on multiple branches of physics. Intensive studies on chaotic phenomena in the last five decades reveal that this kind of complex behavior is much less rare than was initially expected. Pioneering works [12; 13], which searched for algebraically simple chaotic flows, present a number of third-order autonomous mathematical models with only six terms, including scalar nonlinearity and the associated chaotic behavior. After the publication of these works, searching for mathematical models that exhibit chaotic motion became a favorite topic of research studies. Of course, the rusticity of describing a set of ordinary differential equations leads to a simple lumped circuit, which is capable of modelling such dynamics with two active and seven passive elements, as shown in [14]. However, canonical realizations of chaotic oscillators (in the sense of minimum component count) usually have model parameters expressed as functions (generally nonlinear) of the circuit parameters. Typical examples of very simple chaotic flows can be expressed by a single third-order differential equation as previously addressed [15]. Such systems have a direct relation with Newtonian motion dynamics, since individual state variables can be interpreted as position, velocity and acceleration. The implementation of a single higher-order differential equation as an electronic circuit is very simple: the cascade of two-port integrators is put together with multiple feedback branches. A primary assumption, which has only recently been disproven, is that a combination of several saddle-focus [16; 17] equilibrium points is required for the emergence of dense in state space chaotic attractors with a fractal geometric dimension. However, it turns out that saddle-node [18] types of equilibria, with the same stability index as saddle focusses, can also be responsible for the evolution of the chaotic attractor. Finally, after years of research dedicated to the autonomous dynamical systems, it seems that the existence of the multiple fixed points is not necessary for a vector field to exhibit chaotic behavior. Strange attractors can also be observed in dynamical systems with a single unstable node equilibrium, as previously demonstrated [19].