Meng Kit Tang
Chaotic Dynamics: The Three-Body Problem of US–China–Taiwan Relations
In celestial mechanics, the three-body problem refers to the irregular and highly complex motion of three gravitational bodies, for which no general analytic solution exists, even though individual trajectories can be calculated numerically. Liu Cixin’s The Three-Body Problem (2014) helped bring the concept into popular culture, though it is invoked here purely as a metaphor rather than a commentary on geopolitics. Applied to the United States, China, and Taiwan, it highlights how each actor’s diplomatic, military, or economic choices trigger ripple effects that are difficult to foresee and often disrupt expectations of stability.
This stands in contrast to dyadic models in International Relations, which often reduce geopolitical tensions to binary oppositions. The three-body analogy instead captures the volatility of trilateral interactions. For instance, a US arms sale, a Chinese gray zone operation, or a Taiwanese election can shift the balance in ways that are difficult to predict. A bilateral agreement between two powers might temporarily ease tensions between them while simultaneously raising concerns for a third actor, underscoring the reactive and delicate nature of such strategic configurations.
This framework emphasizes complexity over linear causality, casting Taiwan as an active player rather than a passive object. The three-body problem, a classic case in chaos theory, shows how small changes can lead to disproportionate and unpredictable outcomes. Applying this insight to the Taiwan Strait highlights why stability is fragile and disruptions cascade in unexpected ways. Policymaking in such a system must be circumstantial and flexible, with foresight that is adaptive and prepared for ripple effects that cannot be predicted.
Theoretical Context
Traditional International Relations theories - realism, liberalism, and constructivism - often rely on dyadic or linear models that inadequately capture the complexity of trilateral dynamics. Realism tends to reduce Taiwan to a mere pawn in great power rivalry, overlooking its agency and internal politics. Liberalism assumes stable institutional and economic ties, underestimating how quickly shocks, like a contentious election, can disrupt cooperation. Constructivism, while attentive to identity and norms, often frames interactions bilaterally, missing the recursive, multi-directional effects that define trilateral relations.
In contrast, the three-body problem offers a more fitting analogy: it captures how small actions by one actor can cause unpredictable, disproportionate effects throughout the system, reflecting key principles of complexity theory such as feedback loops, emergent behavior, and systemic sensitivity. For instance, a US arms sale to Taiwan under the 2022 Taiwan Enhanced Resilience Act can simultaneously influence China’s military posture and Taiwanese public confidence, creating impacts beyond dyadic frameworks. Unlike realism, which centers on power, or liberalism, which emphasizes cooperation, this approach focuses on interdependent volatility, where each actor’s decisions continuously reshape the entire system. This lens illuminates the Taiwan Strait’s complex geopolitics, as explored further below.
By highlighting chaos and interconnectedness, the three-body framework enriches traditional IR theories and better explains the dynamic geopolitics of the Taiwan Strait. The next section will outline the core assumptions defining this triangular interaction.
Key Assumptions
The US–China–Taiwan triangle rests on three core assumptions:
First, each actor pursues distinct strategic goals as a rational, autonomous player. The United States aims to defend Taiwan under the 1979 Taiwan Relations Act while maintaining strategic ambiguity. China prioritizes unification under the One China principle, shaped in part by domestic nationalism. Taiwan emphasizes democratic self-determination and increasingly asserts its sovereignty.
Second, the system operates in anarchy. With no higher authority to enforce rules and China's UN veto blocking mediation, even minor actions such as a congressional visit or military incursions provoke disproportionate responses. These dynamics resemble the three-body problem, where small shifts produce unpredictable outcomes.
Third, perception is as influential as material power. Distrust or uncertainty about an ally’s commitment can significantly influence decision-making and alter the balance of power.
Together, these assumptions define the triangle as a chaotic system, where events like Taiwan’s 2024 election can trigger cascading effects across the region.
Core Variables and Interdependence
The triangle is shaped by three deeply interwoven variables: power, influence, and conflict. Like celestial bodies in a three-body system, these elements interact in unpredictable and non-linear ways, creating a volatile strategic environment.
Power encompasses military strength, economic influence, and sustained commitments. Recent actions have reinforced defense postures with significant aid pledges, while economic ties remain evident through tariff agreements and major technology deals. A key player’s leadership in a critical industry has attracted various forms of pressure, including cyber threats and talent recruitment efforts. Joint military exercises among regional partners demonstrate resolve but also contribute to heightened tensions and potential risks of escalation.
Influence is exerted through both cooperation and coercion. Taiwan has expanded ties through initiatives like the Global Cooperation and Training Framework, while the US targets Chinese firms with sanctions to constrain Beijing’s global reach. In turn, China offers economic incentives to isolate Taiwan diplomatically and enforce the One China principle.
Conflict often emerges in the gray zone. In the second quarter of 2025, China conducted multiple maritime incursions near the Kinmen Islands and launched operations that disrupted TSMC’s operations through suspected trade secret thefts. Domestically, Taiwan’s legislative gridlock from March to July led to defense budget delays, weakening its deterrence posture.
These forces are tightly coupled. A single move such as an arms sale or economic agreement can shift the balance, triggering unpredictable reactions. The system’s sensitivity to initial conditions mirrors the chaotic dynamics of the three-body problem, where even small changes can destabilize the broader regional order.
Empirical Anchoring: Recent Developments
As abstract as it may seem, the triangular interdependence became visible in 2025 as a cascading chain of events rather than isolated incidents. Four key developments connected to each other, producing feedback loops that reshaped the system’s trajectory.
First, the August 12 extension of the US–China tariff truce kept duties at 30% for US tariffs on Chinese goods and 10% for Chinese tariffs on US goods, preventing a new wave of trade disruption. NVIDIA’s resumption of AI chip exports under a 15% revenue-sharing agreement with Washington temporarily eased tensions between the two powers. This "win" for the two powers, projected to generate over $15 billion in Nvidia sales, intensified pressure on TSMC, which reported acute vulnerabilities from Chinese talent poaching and trade secret thefts, including August detentions of three employees for leaking 2nm chip tech to suspected PRC-linked firms.
What started as a bilateral economic thaw thus perturbed Taiwan's core strategic asset, eroding its global supply chain leverage and inviting Beijing's opportunistic gray zone escalation.
Second, this external pressure coincided with worsening domestic paralysis. From March to July, Taiwan’s split legislature engaged in partisan deadlock, culminating in a failed mass recall vote on July 26 targeting 24 opposition lawmakers. The gridlock delayed critical budget approvals and procurement decisions, which analysts warned weakened deterrence precisely as Chinese gray zone pressure intensified.
Third, Beijing appeared to exploit this window of vulnerability by escalating its coercive measures. In April, the China Coast Guard conducted six incursions into Kinmen’s restricted waters, while air incursions peaked at 76 aircraft and 15 vessels in a single month. These actions kept Taiwan’s military on constant alert, raising operational costs and reinforcing the perception of siege.
Finally, these developments fed into Taiwanese perceptions of alliance risk. A May 2025 poll showed that more than 40% of respondents doubted Washington’s reliability under the Trump administration, a sentiment exacerbated by a July 3% tariff increase on Taiwanese goods and inconsistent signaling from US officials. Public skepticism further constrained Taipei’s policy options, as leaders faced pressure to hedge rather than fully align with Washington.
Taken together, these were not separate events but a reinforcing loop: US–China economic calm exposed Taiwan, domestic gridlock left gaps unfilled, Chinese coercion intensified, and public trust eroded; capturing the three-body system’s tendency to magnify shocks rather than absorb them.
Chaotic Interactions and Sensitivity to Initial Conditions
In this triangular system, seemingly small events can create ripples that lead to outsized consequences due to the simultaneous interplay of the United States, China, and Taiwan’s domestic and foreign policies.
For example, Taiwan’s 2024 election of President Lai Ching-te, seen by many as a pro-independence signal, prompted China to launch its “Joint Sword” military exercises, involving 66 naval vessels and 30 aircraft near Taiwan’s waters, heightening tensions across the Strait. Likewise, a January 2025 US statement emphasizing “strategic clarity” in Taiwan’s defense sparked strong diplomatic protests from China and a 15 percent increase in Chinese patrols in the Bashi Channel.
Historical precedents, such as the 1996 Taiwan Strait Crisis and the 2022 Pelosi visit demonstrate how specific actions like elections, official visits, or political rhetoric can provoke direct responses. However, it is important not to conflate these relatively straightforward interactions with the deeper complexity arising from the triangular relationship among Taiwan, China, and the U.S. The true complexity lies in the simultaneous interplay of these three actors, each with distinct domestic political pressures and foreign policy goals, creating a kind of “three-body problem.”
This dynamic produces unpredictable ripple effects that are difficult to analytically integrate, as shifts in one country’s domestic or international posture can trigger unforeseen consequences in the others. For example, Taiwan’s 2025 legislative deadlock, which delayed defense funding amid the July recall vote, further added instability, encouraging China’s gray zone tactics and underscoring the intricate challenges of managing this multifaceted regional environment.
These examples highlight that in this non-linear and interconnected system; small triggers can cascade unpredictably. This reality calls for flexible and responsive policy approaches to avoid unintended escalations.
The Fragile, Dynamic Status Quo
Despite ongoing tensions and periodic flare-ups, the United States, China, and Taiwan all seem aware of the heavy costs that a full-scale conflict would bring. None of the three appears willing to push the situation into open confrontation, understanding that the risks are simply too great.
For example, the US has tried to manage its commitment through initiatives like the Taiwan Enhanced Resilience Act (TERA), to reassure Taiwan without overtly provoking China. Still, this balance is fragile. 59.6 percent of Taiwanese surveyed remain doubtful about whether the US would take decisive action if a crisis arose. At the same time, China’s ongoing gray zone tactics and Taiwan’s defense budget cuts interact in subtle but destabilizing ways. These dynamics show that what is often called the “status quo” is not a stable condition, but rather a delicate and continuously renegotiated arrangement.
Scenarios and Strategic Uncertainty
The triangular relationship defies simple predictions, but exploring possible future scenarios helps reveal both risks and opportunities in this volatile system.
One potential path is managed de-escalation in 2026. Here, a crisis hotline modeled after Cold War-era frameworks helps ease tensions during a dispute over patrols in the Bashi Channel. Expanded tariff truces, including a $3 billion chip export deal, reduce economic friction and lead to a 20 percent drop in China’s gray zone incursions. Meanwhile, Taiwan’s New Southbound Policy strengthens ties with ASEAN countries, contributing to temporary stability.
Another possibility is accidental escalation. A collision between a Chinese coast guard vessel and a US–Taiwan patrol near Kinmen sparks missile tests by China and disrupts $50 billion in regional trade. In response, US sanctions raise the stakes, risking a wider trade conflict. Taiwan’s $1.2 billion defense budget cut limits its ability to respond effectively, further destabilizing the situation.
The third scenario is a diplomatic setback in 2027. Taiwan’s bid for UN observer status, supported by the US, leads China to withdraw from chip export agreements and increase maritime patrols by 30 percent, raising fears of potential invasion.
Throughout these scenarios, strategic ambiguity remains a double-edged sword, intensifying uncertainty and the risk of miscalculation in an already unstable system.
Taiwan’s Agency and Centrality
Taiwan is not a passive player caught between larger powers; its internal politics actively shape the triangular system. The 2024 election of President Lai Ching-te sparked Chinese military exercises and a US arms sale, while 2025 legislative gridlock and a failed recall vote signaled weakness, prompting more Chinese incursions. Rising public doubt about US support pushed Taiwan to diversify economically, increasing trade with ASEAN and reducing dependence on China.
These actions of elections, budget choices, and economic diversification serve as tipping points, influencing both US and Chinese strategies. Taiwan’s agency thus plays a key role in both stabilizing and unsettling this complex, chaotic dynamic.
Policy Implications and Limits of Prediction
The three-body problem analogy, distinct from strategic triangle theory, highlights how linear predictions fall short in the US–China–Taiwan triangle, where small moves can trigger unpredictable crises. Unlike strategic triangles, which assume structured roles and alignments, this framework emphasizes chaotic, non-linear dynamics, underscoring systemic volatility over predictable patterns.
This means policymakers must prioritize flexible, adaptive strategies to manage the system’s inherent volatility. Practical measures like real-time crisis hotlines can prevent miscalculations, while structured economic dialogues such as coordinated chip supply chains help stabilize fragile trade relationships. Ongoing diplomatic reassurance, including clear commitments under existing agreements, is vital to address skepticism among key actors.
Given the system’s inherent volatility, scenario-driven planning that anticipates events like naval collisions or UN observer bids is crucial. Viewing uncertainty as a fundamental feature rather than a weakness helps policymakers better navigate shocks and sustain temporary stability in this complex trilateral system.
Conclusion
The U.S.–China–Taiwan relationship can be understood as a “three-body problem,” where the interactions among the three actors create a complex and often unpredictable system. Taiwan’s 2024 election and the 2025 legislative deadlock illustrate how domestic events can intensify regional instability. This complexity challenges traditional linear international relations models and underscores the need for flexible policy tools such as crisis hotlines and coordinated economic measures that can adapt to rapidly shifting dynamics. Accepting this inherent uncertainty is essential for developing strategies that effectively manage tensions in this delicate geopolitical environment.
