Dynamical behavior of a new piecewise-linear continuous-time three-dimensional autonomous chaotic system is studied. System equilibria and their stabilities are discussed. Routes to chaos and bifurcations of the system are demonstrated with various numerical examples, where the chaotic features are justified numerically via computing the system fractal dimensions, Lyapunov exponents and power s...

The purpose of this paper is to summarise the 1998 paper by William A. Brock and Cars H. Hommes, ”Heterogeneous beliefs and routes to chaos in a simple asset pricing model”, in Journal of Economic Dynamics and Control, 22, 1235-1274 (Brock and Hommes 1998).

Structural phase transitions may lead from a high temperature disordered phase with a space group Go and a unit cell edge a to: a) A ferrodistortive commensurate ordered state with a space group G1 and an unchanged unit cell, a' = a. b) An antiferrodistortive commensurate ordered state with a space group G2 and a unit cell size which is an integral multiple of the high temperature unit cell: a'...

Optical nonlinearities, such as thermo-optic mechanisms and free-carrier dispersion, are often considered unwelcome effects in silicon-based resonators and, more specifically, optomechanical cavities, since they affect, for instance, the relative detuning between an optical resonance and the excitation laser. Here, we exploit these nonlinearities and their intercoupling with the mechanical degr...

This paper applies machine learning and the mathematics of chaos to the task of designing indoor rock-climbing routes. Chaotic variation has been used to great advantage on music and dance, but the challenges here are quite different, beginning with the representation. We present a formalized system for transcribing rock climbing problems, then describe a variation generator that is designed to...

In this paper we have studied the dynamics of a non driven circuit of fourth-order. The circuit constitutes of two active elements, one linear negative conductance and one non linear resistor exhibiting a symmetrical piecewise linear v-i characteristic. The resistor R1, which couples the negative conductance and the nonlinear element, serves as the control parameter of the system. We have obser...

This paper applies machine learning and the mathematics of chaos to the task of designing indoor rock-climbing routes. Chaotic variation has been used to great advantage on music and dance, but the challenges here are quite different, beginning with the representation. We present a formalized system for transcribing rock climbing problems, then describe a variation generator that is designed to...

We consider the dynamical effects of electromagnetic flux on discrete Chialvo neuron model. It is shown that model can exhibit rich behaviors such as multistability, firing patterns, antimonotonicity, closed invariant curves, various routes to chaos, and fingered chaotic attractors. The system enters a chaos regime via period-doubling cascades, reverse route, curve chaos. results were confirmed...

Criteria usually used by economists to evaluate the accuracy of forecasts generated by a model are based on mean and quadratic errors. The ability to give directional forecast, raise or drop, is not very used whereas it is of big practical interest. If a model was able to give good directional forecasts with a rate greater than 50% over long periods, trading strategies with excess return could ...