ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

For citation:

Zaamoune F., Zerimeche H., Ibrahim R. W., Karimov A. I. Scalable Fixed-Time Synchronization of Robotic Swarms via a Novel 4D Fractional-Order System without Equilibrium Points and with Bistable Dynamics. Izvestiya VUZ. Applied Nonlinear Dynamics, 2026, vol. 34, iss. 3, pp. 349-370. DOI: 10.18500/0869-6632-003219, EDN: XEKTRW

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Language: 
Russian
Heading: 
Bifurcation in Dynamical Systems. Deterministic Chaos. Quantum Chaos.
Article type: 
Article
UDC: 
530.182
DOI: 
10.18500/0869-6632-003219
EDN: 
XEKTRW

Scalable Fixed-Time Synchronization of Robotic Swarms via a Novel 4D Fractional-Order System without Equilibrium Points and with Bistable Dynamics

Autors: 
Zaamoune Faiza, University of Biskra
Zerimeche Hadjer, Constantine 1-Mentouri University
Ibrahim Rabha Waell, Al-Ayen University
Karimov Artur Iskandarovich, St. Petersburg Electrotechnical University “LETI”
Abstract: 

Chaotic systems without equilibrium points represent a significant class of nonlinear dynamical systems because their behavior cannot be interpreted through conventional equilibrium-based analysis. In this study, a novel four-dimensional fractional-order chaotic system without equilibrium points is proposed and analyzed.

The results reveal bistable dynamics characterized by the coexistence of two distinct attractors under the same parameter set and different initial conditions, including symmetric limit cycles and chaotic attractors with different geometric structures. These dynamical features are exploited to enhance trajectory unpredictability in autonomous mobile robotic applications. Furthermore, a fixed-time synchronization framework is developed for large-scale multi-agent systems. In contrast to conventional asymptotic methods, the proposed strategy ensures convergence within a prescribed time bound independent of the initial states. The framework is then implemented in a masterslave robotic swarm, linking fractional-order reference dynamics with integer-order kinematic agents. Numerical investigations confirm the capability of the proposed method to achieve accurate synchronization and reliable trajectory tracking in networked robotic systems.
 

Key words: 
fractional-order calculus
bistable dynamics
no-equilibrium system
fixed-time synchronization swarm robotics
Acknowledgments: 
This study was supported by the Russian Science Foundation, project number 24-71-10064.
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Received: 
11.03.2026
Accepted: 
14.04.2026
Available online: 
21.04.2026
Published: 
29.05.2026
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