## 1 Introduction  
With the increasingly rapid advances of Mars exploration, how to convert Mars resources into propellants and life support consumables has attracted great attention [1, 2]. As the most abundant component in the Martian atmosphere [3], CO\({}_{2}\) can be used as a feedstock for In Situ Resource Utilization (ISRU) to produce CO and O\({}_{2}\)[4]. The O\({}_{2}\) could provide materials for life support and improve the Martian atmosphere, and CO has been proposed for the production of spacecraft propellants [5, 6]. The ISRU can reduce the launch mass of space vehicles and lower the risk of crew and space missions. However, due to the high stability of CO\({}_{2}\) molecules, substantial thermal energy input is required in the decomposition of CO\({}_{2}\), which is a great challenge for ISRU of CO\({}_{2}\) on Mars. It is possible to convert CO\({}_{2}\) into chemicals and fuels using traditional approaches such as thermal catalysis, but the main issues are high energy consumption and low productivity [7]. In fact, non-thermal plasma is an effective technology for molecular activation, the energetic electrons produced in the non-thermal plasma are capable of breaking the double bonds (O=C=O) in CO\({}_{2}\) molecules at a low temperature without heating the entire gas, effectively reducing the energy consumption [8]. In addition, the Martian environment has many advantages for the local decomposition of CO\({}_{2}\) using non-thermal plasma. On the one hand, the average atmospheric pressure on Mars is only 4.5 Torr, which is considered to be close to the ideal for plasma reforming and can make CO\({}_{2}\) gas easy to be ignited at a lower voltage [9; 10; 11]. On the other hand, the low temperature of the Martian atmosphere with an average value of about 210 K can limit the gas heating effect and enhance vibrational up-pumping along the asymmetric stretching mode, which is considered the most efficient approach for the decomposition of CO\({}_{2}\)[12; 13]. In addition, the cold surrounding atmosphere can also slow down the reaction of the recombination of CO and O to generate CO\({}_{2}\)[11]. In addition, a small amount of N\({}_{2}\) (about 2.7%) and Ar (about 1.6%) in the Martian atmosphere facilitate the decomposition of CO\({}_{2}\) molecules. N\({}_{2}\) could transfer vibrational energy to CO\({}_{2}\) molecules, which pumps CO\({}_{2}\) molecules into asymmetric stretching modes [14], Ar could slightly improve the electron energy distribution function (EEDF), enhancing the electron impact processes [15]. Furthermore, the extreme flexibility and immediate switch of non-thermal plasma enable the harvesting of energy from solar power [16; 17]. At present, a large number of studies have discussed the decomposition of CO\({}_{2}\) under atmospheric pressure by using plasma technology [18; 19; 20; 21; 22; 23; 24], which lays the groundwork for investigating CO\({}_{2}\) conversion under Martian conditions. Due to the widespread applications in the industrial fields, dielectric barrier discharge (DBD) has attracted wide-ranging interest in CO\({}_{2}\) conversion and has become one of the most potential candidates for ISRU [25; 26; 27]. However, as a typical nonlinear dynamical system, DBD can possess abundant temporal nonlinear behaviors such as asymmetric discharge, quasiperiodicity, period-doubling bifurcation, and chaos [28; 29; 30; 31]. Through the experimental measurements, [PERSON] et al. [32] reported that, by increasing the amplitude of voltage, the discharge in atmospheric helium can undergo an inverse period-doubling bifurcation from chaotic state to period-one state. [PERSON] et al. [33] investigated the temporal nonlinear behaviors in argon atmospheric DBDs based on a fluid model, and found that, by increasing the driving frequency, the discharge can enter chaotic discharge via a period-doubling bifurcation and then return stable periodic discharge via an inverse period-doubling bifurcation. The simulation results of [PERSON] et al.