I am looking for some specific parameter(s) with which non linearity can be quantified in terms of its degree of complexity.Thank you so much for above replies. Sir, I dint get the right hit through Google for soft copy of mentioned book @ Prof. Ljubomir Jacic.
I'm afraid that such parameters you are looking for do not exist. Of course there are a lot of special results for special types of nonlinearities. For example, there is a list of sytems (of ODEs) known to be 'integrable' in the sense of Liouville, so that the dynamic behavious boils down to quasiperiodic movement on some torus T^n. And if you start with an integrable system, the Kolmogorov-Arnol'd-Moser theorem gives criteria for a system to be 'sufficiently close', which guarantees the persistence of quasiperiodic movements.
In general, you might want to measure the complexity of the solutions of a system of nonlinear ODEs, which could mean quite different things (e.g. 'counting' prime periodic orbits, homoclinic orbits, ergodicitiy properties; depends on what you are interested in.) I would, however, not agree that 'stiffness' measures the complexity of a nonlinearity. It rather measures how numerically tractable the problem is.
Agree with Stefan Born at all! If book is not available via internet, try by some library. Prof. Siljak was wit dept.of EE in Santa Clara, Ca, USA. My book is about 30 years old! :)
I believe Kumar wants a number that will say this system is more chaotic than the other one. Such has not been found to the best of my knowledge. However, you can explore parameters such as correlation dimension, hurst exponent, hjorth parameter, entropy. Most of this are for nonlinear time series. If you need reference materials, kindly inbox me so i can mail some to you.
http://www.tandfonline.com/doi/abs/10.1080/00986449808912379?journalCode=gcec20 Try this source from link. It may be the real one! Here it is NONLINEARITY QUANTIFICATION AND ITS APPLICATION TO NONLINEAR SYSTEM IDENTIFICATION
One can linearize the nonlinear equation around the original nonlinear trajectory. This is often done in Numerical Weather Prediction. The trajectory, linearized around the nonlinear, is called tangent linear.
An Efficient Measure for Quantification of Nonlinearity in Chemical Engineering Processes Based on I/O Steady-State Loci!
Nonlinearity is virtually ubiquitous in chemical engineering plants, and assessing the degree of nonlinearity involved in a process is of special interest for process control purposes. In this paper, we introduce a simple nonlinearity measure to quantify the extent of nonlinearity in a dynamic system based on its normalized steady-state input/output loci. Our nonlinearity measure obviates the limitations of previous metrics in terms of computational effort and correct identification of highly nonlinear relationships. The measure is satisfactorily applicable to various I/O relationships—from truly linear to sinusoidal, for instance. In order to illustrate the efficiency of the proposed measure, four numerical examples concerning a double-effect evaporator, a jacketed continuously stirred tank reactor (CSTR) with an irreversible reaction, a CSTR involving van de Vusse reactions, and the Henson–Seborg–Pottmann CSTR are presented...