Measure of Departure from Conditional Symmetry Based on Cumulative Probabilities for Square Contingency Tables

For the analysis of square contingency tables with ordered categories, a measure was developed to represent the degree of departure from the conditional symmetry model in which there is an asymmetric structure of the cell probabilities with respect to the main diagonal of the table. The present paper proposes a novel measure for the departure from conditional symmetry based on the cumulative probabilities from the corners of the square table. In a given example, the proposed measure is applied to Japanese occupational status data, and the interpretation of the proposed measure is illustrated as the departure from a proportional structure of social mobility.

Conditional Symmetry of a Memristive System with Amplitude and Frequency Modulation Control

In this study, we studied the effects of offset boosting on the memristive chaotic system. A system with symmetry and conditional symmetry was constructed, by adding the absolute value function to an offset boosting system. It is proved that the symmetric system or a conditionally symmetric system can be constructed with similar or the same dynamic characteristics by using certain correction and offset boosting in an asymmetric system. In addition to multiple stability, the memristive system can also realize the amplitude and frequency control by introducing a parameter. The simulation circuit verifies the amplitude modulation characteristics of the system.

Classical and quantum $$(2+1)$$-dimensional spatially homogeneous string cosmology

We introduce three families of classical and quantum solutions to the leading order of string effective action on spatially homogeneous $$(2+1)$$ ( 2 + 1 ) -dimensional space-times with the sources given by the contributions of dilaton, antisymmetric gauge B-field, and central charge deficit term $$\varLambda $$ Λ . At the quantum level, solutions of Wheeler–DeWitt equations have been enriched by considering the quantum versions of the classical conditional symmetry equations. Concerning the possible applications of the obtained solutions, the semiclassical analysis of Bohm’s mechanics has been performed to demonstrate the possibility of avoiding the classical singularities at the quantum level.

Hidden Attractors with Conditional Symmetry

By introducing an absolute value function for polarity balance, some new examples of chaotic systems with conditional symmetry are constructed that have hidden attractors. Coexisting oscillations along with bifurcations are investigated by numerical simulation and circuit implementation. Such new cases enrich the gallery of hidden chaotic attractors of conditional symmetry that are potentially useful in engineering technology.

Symmetry Evolution in Chaotic System

A comprehensive exploration of symmetry and conditional symmetry is made from the evolution of symmetry. Unlike other chaotic systems of conditional symmetry, in this work it is derived from the symmetric diffusionless Lorenz system. Transformation from symmetry and asymmetry to conditional symmetry is examined by constant planting and dimension growth, which proves that the offset boosting of some necessary variables is the key factor for reestablishing polarity balance in a dynamical system.

Time-Reversible Chaotic System with Conditional Symmetry

When the polarity reversal induced by offset boosting is considered, a new regime of a time-reversible chaotic system with conditional symmetry is found, and some new time-reversible systems are revealed based on multiple dimensional offset boosting. Numerical analysis shows that the system attractor and repellor have their own dynamics in respective time domains which constitutes the fundamental property in a time-reversible system. More remarkably, when the conditional symmetry is destroyed by a slightly mismatched offset controller, the system undergoes different bifurcations to chaos, and the corresponding coexisting attractors and repellors shape their own phase trajectories.