https://doi.org/10.1140/epjs/s11734-021-00136-7
Regular Article
Symmetry-breaking, amplitude control and constant Lyapunov exponent based on single parameter snap flows
1
Research Unit of Laboratory of Condensed Matter, Electronics and Signal Processing (UR-MACETS) Department of Physics, Faculty of Sciences, University of Dschang, P.O. Box 67, Dschang, Cameroon
2
Department of Physics, University of Mons, Place du Parc 20, 7000, Mons, Belgium
3
School of Physics and Electronics, Central South University Changsha, 410083, Hunan, China
4
Research Unit of Laboratory of Automation and Applied Computer (LAIA), Electrical Engineering Department of IUT-FV, University of Dschang, P.O. Box 134, Bandjoun, Cameroon
5
Department of Electrical and Electronic Engineering, College of Technology (COT), University of Buea, P.O. Box 63, Buea, Cameroon
6
Department of Electrical and Electronic Engineering, Faculty of Engineering and Technology (FET), University of Buea, P.O. Box 63, Buea, Cameroon
Received:
27
December
2020
Accepted:
28
April
2021
Published online:
5
June
2021
In this paper, we introduce a novel snap system with a unique parameterized piecewise quadratic nonlinearity in the form 
where n controls the symmetry of the system and serves as total amplitude control of the signals. The model is described by a continuous time 4D autonomous system (ODE) with smooth conditional nonlinearity. We study the chaos mechanism with respect to system parameters both in the symmetric and asymmetric modes of oscillations by exploiting bifurcation diagrams, basin of attractions and phase portraits as main tools. In particular, for
, the system displays a perfect symmetry and develops rich dynamics including period doubling sequences, merging crisis, hysteresis, and coexisting multiple symmetric attractors. For
, the system is non-symmetric and the space magnetization induced more complex and striking effects including asymmetric double scroll strange attractors, parallel branches, and asymmetric basin boundary leads to many coexisting asymmetric stable states and so on. Apart from all these complex and rich phenomena, many others including offset-boosting with total amplitude control, and antimonotonicity are also presented. Finally, Pspice based simulations of the proposed system are included.
© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2021
