**Nonlinear system theory: Another look at dependence**

Based on the scheme theory, we tend to introduce antecedently undescribed dependence measures for stationary causative processes. Our physical and prophetical dependence measures quantify the degree of dependence of outputs on inputs in physical systems. The projected dependence measures offer a natural framework for a limit theory for stationary processes. above all, underneath conditions with quite easy forms, we tend to gift limit theorems for partial sums, empirical processes, and kernel density estimates. The conditions ar delicate and simply verifiable as a result of they’re directly associated with the data-generating mechanisms. **[1]**

**A bibliography on nonlinear system identification**

The present list represents a comprehensive list of references on system identification and its applications in signal process, communications, and medicine engineering. a trial has been created to form this list complete by listing most of the prevailing references up to the year 2000 and by providing a close classification cluster. **[2]**

**Nonlinear system modeling based on the Wiener theory**

This paper may be a tutorial of system modeling strategies that area unit supported the Wiener theory of nonlinear systems. the fundamental ideas that underlie the Wiener theory area unit mentioned and illustrated. numerous modeling strategies area unit conferred by that a non-linear system are often sculpturesque mistreatment either white mathematician, nonwhite mathematician, or sure non-Gaussian inputs. The experimental error in crucial the Wiener model is mentioned in terms of a brand new idea known as activity stability. Since tries area unit being created to use these modeling strategies to various areas of study, this paper is written to be comprehensible by nonspecialists in system theory.** [3]**

**New Type of Spectral Nonlinear Resonance Enhances Identification of Weak Signals**

Some nonlinear systems possess innate capabilities of enhancing weak signal transmissions through a novel method referred to as random Resonance (SR). However, existing SR mechanism suffers restricted signal sweetening from inappropriate entraining signals. Here we have a tendency to propose a replacement and effective implementation, leading to a replacement variety of spectral resonance the same as SR however capable of achieving orders of magnitude higher signal sweetening than antecedently rumored. By using entraining frequency within the vary of the weak signal, robust spectral resonances will be evoked to facilitate nonlinear modulations and intermodulations, thereby strengthening the weak signal. **[4]**

**Vibration Reduction of Two Degree of Freedom Nonlinear System Subject to Parametric Excitation via Negative Feedback Velocity**

Negative speed controller (NVC) is employed to cut back the vibration of a 2 degree of freedom scheme subjected to constant excitation forces. The moving motion of the system represented by 2 coupled equation, the worst resonance case of the system close to the sub-harmonic resonance (ω ≃ 2ω2 ). the strategy of multiple scales perturbation technique (MSPT) is applied to get the periodic response equation close to the chosen resonance case. Study the controls on the worst resonance case numerically. the soundness of the obtained numerical answer is investigated mistreatment each section plane strategies and frequency response equations. Effects of various parameters on the system behavior square measure studied numerically. **[5]**

**Reference**

**[1]** Wu, W.B., 2005. Nonlinear system theory: Another look at dependence. Proceedings of the National Academy of Sciences, 102(40), (Web Link)

**[2]** Giannakis, G.B. and Serpedin, E., 2001. A bibliography on nonlinear system identification. Signal Processing, 81(3), (Web Link)

**[3]** Schetzen, M., 1981. Nonlinear system modeling based on the Wiener theory. Proceedings of the IEEE, 69(12), (Web Link)

**[4]** New Type of Spectral Nonlinear Resonance Enhances Identification of Weak Signals

Rongming Lin, Teng Yong Ng & Zheng Fan

Scientific Reports volume 9, Article number: 14125 (2019) (Web Link)

**[5]** A. Amer, Y., & M. Agwa, M. (2019). Vibration Reduction of Two Degree of Freedom Nonlinear System Subject to Parametric Excitation via Negative Feedback Velocity. Asian Research Journal of Mathematics, 12(1), (Web Link)