## 1. INTRODUCTION

Dissipative systems with a nonlinear time-delayed feedback or memory can produce chaotic dynamics [1, 2]. The effect of the delay on the dimension of these chaotic attractors is shown [3]. Delay systems generically have families of periodic solutions, which are reappearing for infinitely many delay times. As delay increases, the solution families overlap leading to increasing coexistence of multiple stable as well as unstable solutions [4]. Anticipating chaotic synchronization is discussed [5].

Packard [6] showed adaptation to the edge of chaos in cellular automata rules with genetic algorithms. Some of his results were later disputed [7]. Coevolution to the edge of chaos is discussed in Ref. 8. Edge of chaos has been found to be the optimal setting for control of a system [9]. A self-adjusting system is a system in which the control of a parameter value depends on previous states of the system [10]. The authors [11] describe adaptation to the edge of chaos in logistic map. They believe that adaptation to the edge of chaos is a generic property of the systems with a low-pass filtered feedback. They believe that this property is independent of the form of the feedback and the system under study. The findings have also been confirmed experimentally with Chua's circuit [12]. In Ref. 13 conserved quantities are used for investigating adaptation to the edge of chaos. The phrase *Edge of Chaos* was originally proposed by Chris Langton in 1990 in the area of cellular automata [14] although some others mentioned the same concept around the same time [15]. Guiding an adaptive system through chaos is also considered [16]. Adaptation to the edge of chaos is studied [17]. In that research, one-dimensional chaotic maps are used as dynamical systems and feedback of values obtained from observations of the system variable are provided for the system. The parameter changes more slowly than the variable. The authors believe that separation of time scales is necessary for the method to be self-contained without external control. The parameter governs the dynamics of the variable every certain number of steps of time series. Conversely, the variables of the system determine the dynamics of the parameter. Extinction in a simple ecological model is shown [18]. It is stated that chaotic dynamics does not necessarily lead to population extinction. The topic is also discussed in other source [19–22].

### 1.1. Purpose of this Research

We are studying coupled oscillators. We study the case in which we interfere with the coupling and for this case, we use the concept of forced oscillators and use mechanical metronomes placed on a rigid base. We study the effects of movements of the base on the dynamics of the oscillators. This makes the whole set a dynamical system which contains two subsystems (the oscillators) that has many potentials to be explored. We will consider the case where the system can adjust itself; In other words, we study how the system evolves in time when some parameters of the system are adjusted by states of the system itself.