Chaos emerging in soil failure patterns observed during tillage: Normalized deterministic nonlinear prediction (NDNP) and its application

Abstract

Real-world processes are often combinations of deterministic and stochastic processes. Soil failure observed during farm tillage is one example of this phenomenon. In this paper, we investigated the nonlinear features of soil failure patterns in a farm tillage process. We demonstrate emerging determinism in soil failure patterns from stochastic processes under specific soil conditions. We normalized the deterministic nonlinear prediction considering autocorrelation and propose it as a robust way of extracting a nonlinear dynamical system from noise contaminated motion. Soil is a typical granular material. The results obtained here are expected to be applicable to granular materials in general. From a global scale to nano scale, the granular material is featured in seismology, geotechnology, soil mechanics, and particle technology. The results and discussions presented here are applicable in these wide research areas. The proposed method and our findings are useful with respect to the application of nonlinear dynamics to investigate complex motions generated from granular materials.

Heteroclinic cycles in a new class of four-dimensional discontinuous piecewise affine systems

“…It has many potential applications in engineering fields, such as biology, mechanical engineering, private communication, and artificial intelligence. [1][2][3][4][5][6][7][8][9][10][11][12][13] Since 1963, Lorenz put his research findings, [14] the first physical evidence of chaos, into the public article, various researchers all over the world sparked off a craze for studying chaotic behaviors. A lot of achievements [15][16][17][18][19][20][21] have been made in the chaotic field.…”